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ELEMENTARY LESSONS 



ELECTEICITY AND MAGNETISM 



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Epoch 



•=^^■,.--20°^^' A^D^£900. 




IValker &• Boutall sc 

MAGNETIC CHART OF THE BRITISH ISLANDS, 

SHOWING THE LINES OF EQUAL 3IAGNETIC DECLINATION AND 
THOSE OF EQUAL MAGNETIC DIP. 



ELEMENTAEY LESSONS 



ELECTKICITY & MAGNETISM 



SILVANUS P. THOMPSON, 

D.Sc, B.A., F.K.S., F.E.A.S. 

PKnHCIPAL OF AlfD PEOFESSOR OF PHYSICS IN THE CITY AND GUILDS OF 

LONDON TECHNICAL COLLEGE, FINSBTJRY ; 

LATE PKOFESSOK OF EXPERIMENTAL PHYSICS IN 

TTNIVEESITY COLLEGE, BRISTOL 



NEW EDITION, REVISED THROUGHOUT 
WITH ADDITIONS 



MACMILLAN AND CO. 

AND LONDON 
1895 

All rights reserved 



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6^-^ 



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Copyright, 1894, 
By MACMILLAN AND CO. 



Norbjootj i3«8S : 

J. S. Gushing & Co. - Berwick & Smith. 

Boston, Mass., U.S.A. 



PREFACE 

These Elementary Lessons have now been largely re- 
written. The considerable changes made have been 
necessitated not only by the progress of the science but 
by the piracy, covert as well as open, to which since its 
appearance in 1881 the book has been subjected. 

In the thnteen years which have elapsed much addi- 
tion has been made to our knowledge, and many points 
then in controversy have been settled. The system of 
electric units, elaborated first by the British Association 
and subsequently in several International Congresses, is 
now legalized in the chief civilized countries, l^ew mag- 
netic surveys — in England by Thorpe and Riicker, in 
the United States under Mendenhall — have enabled new 
magnetic charts to be prepared for the epoch 1900 a.d. 
The researches of Ewing, Hopkinson, and others on the 
magnetic properties of iron, and the general recognition 
of the principle of the magnetic circuit, have advanced 
the science of magnetism, to which also Ewing's molecu- 
lar theory has given an added interest. The properties 
of alternate currents, of which in 1881 little was known, 
have been forced into study by the extension of their 
industrial uses in telephony and in electric lighting. 



viii ELECTRICITY AND MAGNETISM 

Entirely new is the use of polyphase alternate currents 
and rotatory magnetic fields for the electric transmission 
of power. Transformers have come into extensive em- 
ployment for the distribution at low-pressure of electric 
energy which has been transmitted from a generating 
station at high-pressure. Accumulators for the storage 
of electric energy have become of great commercial im- 
portance. Electric lamps, large and small, illuminate in 
millions our cities, towns, villages and ships. Electric 
currents for lighting and power are now supplied publicly 
on a very large scale from central stations operated by 
steam or water power. Supply-meters are in regular use, 
and measuring instruments of many forms have come 
into the market. 

Along with these advances in practice there has been 
a no less striking progress in theory. The ideas of Fara- 
day, as enlarged and developed by Clerk Maxwell, were 
in 1881 only beginning to be understood and appreciated 
outside a narrow circle. In 1894, thanks largely to the 
labours of Heaviside, Hertz, Lodge, Poynting, Fitzgerald, 
Boltzmann, Poincare, and others, they are every\\"here 
accepted. In 1881 Maxwell's electromagnetic theory of 
light — a conception not less far-reaching than the theory 
of the conservation of energy — was deemed of doubtful 
probability : it was not yet accepted by such great masters 
as Lord Kelvin or Von Helmholtz. Though adopted by 
the younger generation of British physicists, it needed the 
experimental researches of Hertz and of Lodge upon the 
propagation of electric waves to demonstrate its truth to 
their brethren in Germany, France, and America. Even 
now, after the most convincing experimental verifications 



PEEFACE ix 

of Maxwell's splendid generalization that light-waves are 
really electric waves, many of the logical consequences of 
Maxwell's teaching are still ignored or misunderstood. 
It is still, to many, a hard saymg that in an electric 
circuit the conducting wire though it guides does not 
carry the energy : that the energy-paths lie outside in 
the sm-rounding medium, not inside within the so-called 
conductor. That the guttapercha sheath, and not the 
copper wii'e within it, is the actual medium which con- 
veys the impulse from one side of the Atlantic to the 
other in cable-telegraphy, is still incredible to those 
brought up in the older school of thought. But it is 
none the less a necessary consequence of the views which 
the inescapable logic of facts drove Maxwell and his 
followers to adopt. 

This expansion of the science and of its practical 
applications has rendered m.ore difficult than before the 
task of presenting wdth sufficient clearness, yet with 
necessary brevity, an elementary exposition of the lead- 
ing phenomena, and of their relations to one another. 

The author is under obligations to many scientific 
friends for data of which he has made use. He is under 
special obligations to his assistant, Mr. Miles Walker, for 
indefatigable proof-reading and revision of the Problems 
and Index. 

London, September 1894. 



CONTENTS 

Part JJirst 

CHAPTER I 

Fkictional Electricity 

LESSON 

I. Electric Attraction and Repulsion 
11. Electroscopes 

III. Electrification by Influence 

IV. Conduction and Distribution of Electricity 
V. Electric Machines ..... 

VI. The Leyden Jar and other Condensers 
VII. Other Sources of Electrification . 



1 
15 
24 
85 

47 
68 

77 



CHAPTER II 
Magnetism 

VIII. Magnetic Attraction and Repulsion ... 89 

IX. Methods of making Magnets .... 99 

X. Distribution of Magnetism 106 

XI. Laws of Magnetic Force 117 

Note on Ways of Reckoning Angles and Solid Angles 133 

XII. Terrestrial Magnetism ..... 136 



Xll 



ELECTRICITY AND MAGNETISM 



CHAPTER III 
Current Electricity 

LESSON PAGE 

XIII. Simple Voltaic Cells 147 

XIV. Chemical Actions in the Cell . . . 157 
XV. Voltaic Cells 163 

XVI. Magnetic Actions of the Current . . .181 

XVII. Galvanometers 193 

XVIII. Currents produced by Induction . . . 210 

XIX. Chemical Actions of the Currents . . 223 
XX. Physical and Physiological Effects of the 

Current 234 



I 



iPart ^ztonH 



CHAPTER IV 

Electrostatics 

XXI. Theory of Potential 244 

Note on Fundamental and Derived Units . 263 

XXII. Electrometers 267 

XXIII. Dielectric Capacity, etc 277 

XXIV. Phenomena of Discharge . . . . 293 
XXV. Atmospheric Electricity .... 316 



CHAPTER V 
Electromagnetics 



XXVI. 


Magnetic Potential 


. 327 


XXVII. 


The Electromagnetic System of Units 


. 344 


XXVIII. 


Properties of Iron and Steel . 


. 354 


XXIX. 


Diamagnetism .... 


. 363 


XXX. 


The Magnetic Circuit . 


. 369 


XXXI. 


Electromagnets .... 


. 374 


XXXII. 


Electrodynamics .... 


. 384 



CONTENTS 



CHAPTER VI 
Measurement of Currents, etc. 

LESSON PAGE 

XXXIII. Ohm's Law and its Consequences . . 397 

XXXIV. Electrical Measurements . . . .412 



CHAPTER VII 
Thermo-Electricity 
XXXV. Thermo-Electric Currents . . . .426 

CHAPTER VIII 

Heat, Power, and Light, from Electric Currents 

XXXVI. Heating Effects of Currents . . .435 
XXXVII. Electric Energy : its Supply and Measure- 
ment ....... 441 

XXXVIII. Electric Motors (Electromagnetic Engines) 448 
XXXIX. Electric Light 455 

CHAPTER IX 

Inductance 

XL. Mutual Induction 464 

XLI. Self-induction 468 

CHAPTER X 
Dynamos and Transformers 



XLII. Magneto-electric and Dynamo-electric Gen 

erators .... 
XLIII. Alternate Currents . 
XLIV. Alternate-current Generators 

XLV. Transformers 
XLVI. Alternate-current Motors . 



476 

486 
495 
500 
504 



XIV ELECTEICITY AXD MAGNETISM 



CHAPTER XI 
Electro-Che3iistrt 

LESSON PAGE 

XL VII. Electrolysis . . . ... . .508 

XLVIII. Accumulators 518 

XLIX. Electrodeposition 520 



CHAPTER Xn 

Telegraphy 

L. Electric Telegraphs 525 

LI. Cable Telegraphy 541 

LII. Miscellaneous Telegraphs .... 543 

CHAPTER XIII 
Telephoxt 
LIII. Telephones . . . ^. . . .547 

CHAPTER XIV 

Electric Waves 

LIV, Oscillations and Waves 554 

LV. The Electromagnetic Theory of Light . . 558 
LVI. Other Relations between Light and Elec- 
tricity ....... 56G 



CONTENTS XV 



APPENDIX 

PAGE 

Appendix A. Table of Angles and Solid Angles 574 
Appendix B. Abstract or Bulletin of U. S. Coast 

AND Geodetic Survey 576 

Appendix C. Official Specification for the 

Preparation of the Clark Standard Cell . 579 

Problems and Exercises ...... 582 

Index 609 

Magnetic Chart of the British Islands Frontispiece 
Magnetic Map of the United States . " 



4 



ELEMENTAKY LESSOKS 

ON 

ELECTRICITY & MAGNETISM 



?Part jFtrgt 



CHAPTER I 

FRICTIONAL ELECTRICITY 

Lesson L — Electric Attraction and Repulsion 

1. Electricity. — Electricity is the name given to an 
invisible agent known to us only by the effects which it 
produces and by various manifestations called electrical. 
These manifestations, at first obscure and even mysterious, 
are now well understood ; though little is yet known of 
the precise nature of electricity itself. It is neither 
matter nor energy ; yet it apparently can be associated 
or combined with matter; and energy can be spent in 
moving it. Indeed its great importance to mankind 
arises from the circumstance that by its means energy 
spent in generating electric forces in one part of a system 
can be made to reappear as electric heat or light or work 
at some other part of the system ; such transfer of energy 
taking place even to very great distances at an enor- 
mous speed. Electricity is apparently as indestructible as 

B 1 



2 ELECTRICITY AND MAGNETISM part i 

matter or as energy. It can neither be created nor 
destroyed, but it can be transformed in its relations to 
matter and to energy, and it can be moved from one place 
to another. In many ways its behaviour resembles that 
of an incompressible liquid ; in other ways that of a 
highly attenuated and weightless gas. It appears to exist 
distributed nearly uniformly throughout all space. Many 
persons (including the author) are disposed to consider it 
as identical with the luminiferous ether. If it be not the 
same thing, there is an intimate relation between the two. 
That this must be so, is a necessary result of the great 
discovery of Maxwell — the greatest scientific discovery of 
the nineteenth century — that light itseK is an electric 
phenomenon, and that the light-waves are merely electric, 
or, as he put it, electromagnetic waves. 

The name electricity is also given to that branch of 
science which deals with electric phenomena and theories. 
The phenomena, and the science which deals with them, 
fall under four heads. The manifestations of electricity 
when standing still are different from those of electricity 
moving or flowing along : hence we have to consider 
separately the properties of (i.) statical charges, and those 
of (ii.) currents. Further, electricity whirling round or in 
circulation possesses properties which were independently 
discovered under the name of (iii.) magnetism. Lastly, 
electricity when in a state of rapid vibration manifests 
new properties not possessed in any of the previous states, 
and causes the propagation of (iv.) ivaves. These four 
branches of the science of electricity are, however, closely 
connected. The object of the present work is to give the 
reader a general view of the main facts and their simple 
relations to one another. 

In these first lessons we begin with charges of 
electricity, their production by friction, by influence, and 
by various other means, and shall study them mainly by 
the manifestations of attraction and repulsion to which 
they give rise. After that we go on to magnetism and 



ELECTRIC ATTRACTION 



currents, and the relations between them. The subject of 
electric waves is briefly discussed at the end of the book. 
2. Electric Attraction. — If j^ou take a piece of seal- 
ing-wax, or of resin, or a glass rod, and rub it upon a 
piece of flannel or silk, it will be found to have acquired 
a property which it did not previously possess : namely, 
the power of atti'acting to itself such light bodies as chaff, 
or dust, or bits of paper (Fig. 1). This curious power 




was originally discovered to be a property of amber, or, 
as the Greeks called it, -rjXeKrpov, which is mentioned by 
Thales of Miletus (b.c. 600), and by Theophrastus in his 
treatise on Gems, as attracting light bodies v^hen rubbed. 
Although an enormous number of substances possess this 
property, amber and jet were the only two in which its 
existence had been recognized by the ancients, or even 
down to so late a date as the time of Queen Elizabeth. 



ELECTRICITY AND MAGNETISM part i 




About the year 1600, Dr. Gilbert of Colchester discovered 

by experiment that not 
only amber and jet, but a 
very large number of sub- 
stances, such as diamond, 
sapphire, rock-crystal, glass, 
sulphur, sealing-wax, resin, 
etc., which he styled eUc- 
trics* possess the same pro- 
perty. Ever since his time 
the name electricity f has 
been employed to denote the 
agency at work in producing 
these phenomena. Gilbert 
also remarked that these ex- 
periments are spoiled b)^ the 
presence of moisture. 
3. Further Experiments. — A better way of observ- 
ing the attracting force is to employ a small ball of elder 
pith, or of cork, hung 
by a fine thread from a 
support, as shown in 
Fig. 2. A dry warm 
glass tube, excited by 
rubbing it briskly with 
a silk handkerchief, 
will attract the pith- 
ball strongly, showing 
that it is highly electri- 
fied. The most suit- 
able rubber, if a stick 
of sealing-wax is used, 
M'ill be found to be 
flannel, woollen cloth, or, best of all, fur. Boyle discovered 

* " Electrica ; quae attrahunt eadem ratione ut electrum " (Gilbert). 
+ The first work in which this terra was used is that of Eobert Boyle, 
On the Mechanical Production of Electricity, pubUshed at Oxford in 1675. 




CHAP. I ELECTKinCATION BY FRICTION 5 

that an electrified body is itself attracted by one that 
has not been electrified. This may be verified (see 
Fig. 3) by rubbing a stick of sealing-wax, or a glass 
rod, and hanging it in a wire loop at the end of a silk 
thread. If, then, the hand be held out towards the 
suspended electrified body, the latter will turn round 
and approach the hand. So, again, a piece of silk ribbon, 
if rubbed with warm indiarubber, or even if drawn 
between two pieces of warm flannel, and then hung up 
by one end, w^ill be found to be attracted by objects 
presented to it. If held near the wall of the room it will 
fly to it and stick to it. With proper precautions it can 
be shown that both the rubber and the thing rubbed are 
in an electrified state, for both will attract light bodies; 
but to show this, care must be taken not to handle the 
rubber too much. Thus, if it is desired to show that 
when a piece of fur is rubbed upon sealing-wax, the fur 
becomes also electrified, it is better not to take the fur in 
the hand, but to cement it to the end of a glass rod as a 
handle. The reason of this precaution wdll be explained 
toward the close of this lesson, and more fully in Lesson 
lY. 

A large number of substances, including iron, gold, 
brass, and aU the metals, when held in the hand and 
rubbed, exhibit no sign of electrification, — that is to say, 
do not attract light bodies as rubbed amber and rubbed 
glass do. Gilbert mentions also pearls, marble, agate, 
and the lodestone, as substances not excited electrically 
by rubbing them. Such bodies were, on that account, 
formerly termed non-electrics ; but the term is erroneous, 
for if they are mounted on glass handles and then rubbed 
with silk or fur, they behave as electrics. 

4. Electric Repulsion. — When experimenting, as in 
Fig. 1, with a rubbed glass rod and bits of chopped paper, 
or straw, or bran, it will be noticed that these little 
bits are first attracted and fly up towards the excited rod, 
but that, having touched it, they are speedily repelled 



ELECTRICITY AND MAGNETISM part i 




and fly back to the table. To show this repulsion better, 

let a small piece of feather or down be hung by a silk 

thread to a support, and 
let an electrified glass rod 
be held near it. It will 
dart towards the rod and 
stick to it, and a moment 
later will dart away from 
it, repelled by an mvisible 
force (Fig. 4), nor will it 
again dart towards the 
rod. If the experiment 
be repeated with another 
feather and a stick of 
sealing-wax rubbed on 
flannel the same effects 
will occur. But, if now 
the hand be held towards 
the feather, it will rush 

toward the hand, as the rubbed body (in Fig. 3) did. 

This proves that the feather, though it has not itself been 

rubbed, possesses the 

property originally 

imparted to the rod 

by rubbing it. In 

fact, it has become 

electrified, by having 

touched an electrified 

body which has given 

part of its electricity 

to it. It would ap- 
pear then that two 

bodies electrified with 

the same electrifica- 

tion repel one an- 
other. This may be confirmed by a further experiment. 

A rubbed glass rod, hung up as in Fig 3, is repelled by a 



Fig. 4. 




OPPOSITE ELECTRIC STATES 



similar rubbed glass rod ; while a rubbed stick of sealing- 
wax is repelled by a second rubbed stick of sealing-wax. 
Another way of showing the repulsion between two 
similarly electrified bodies is to hang a couple of small 
pith-balls, by thin linen threads to a glass support, as 
in Fig. 5, and then touch them both with a rubbed glass 
rod. They repel one another and fly apart, instead of 
hanging down side by side, while the near presence of 
the glass rod will make them open out still wider, for 
now it repels them both. The self-repulsion of the parts 
of an electrified body is beautifully illustrated by the 
experiment of electrifying a soap-bubble, which expands 
when electrified. 

5. Two Kinds of Electrification. — Electrified bodies 
do not, however, always repel one another. The feather 
which (see Fig. 4) has been touched by a rubbed glass 
rod, and which in consequence is repelled from the 
rubbed glass, will be attracted if a stick of rubbed seal- 
ing-wax be presented to it ; and conversely, if the feather 
has been first electrified by touching it with the rubbed 
sealing-wax, it will be attracted to a rubbed glass rod, 
though repelled by the rubbed wax. So, again, a rubbed 
glass rod suspended as in Fig. 3 will be attracted by a 
rubbed piece of sealing-wax, or resin, or amber, though 
repelled by a rubbed piece of glass. The two pith-balls 
touched (as in Fig. 5) with a rubbed glass rod fly from 
one another by repulsion, and, as we have seen, fly wider 
asunder when the excited glass rod is held near them ; 
yet they fall nearer together when a rubbed piece of 
sealing-wax is held under them, being attracted by it. 
Symmer first observed such phenomena as these, and 
they were independently discovered by Du Fay, who 
suggested in explanation of them that there were two 
different kinds of electricity which attracted one another 
while each repelled itself. The electricity produced on 
glass by rubbing it with silk he called vitreous electricity, 
supposing, though erroneously, that glass could yield no 



8 ELECTRICITY AND MAGNETISM part i 

other kind ; and the electricity excited in such subst mces 
as sealing-wax, resin, shellac, iiidiarubber, and amber, 
by rubbing them on wool or flannel, he termed resinous 
electricity. The kind of electricity produced is, however, 
found to depend not only on the thing lubbed but on the 
rubber also ; for glass yields " resinous " electricity when 
rubbed with a cat's skin, and resin yields "vitreous" 
electricity if rubbed with a soft amalgam of tin and 
mercury spread on leather. Hence these names have 
been abandoned in favour of the more appropriate terms 
introduced by Franklin, who called the electricity^ excited 
upon glass by rubbing it with siYk positive electricity, and 
that produced on resinous bodies by friction with wool or 
fur, negative electricity. The observations of Symmer 
and Du Fay may therefore be stated as follows: — Two 
positively electrified bodies apparently repel one another: 
two negatively electrified bodies apparently repel one 
another: but a positively electrified body and a negatively 
electrified body apparently attract one another. It is 
now known that these effects which appear like a repul- 
sion and an attraction between bodies at a distance from 
one another are really due to actions going on in the 
medium between them. The positive charge does not 
really attract the negative charge that is near it; but 
both are urged toward one another by stresses in the 
medium in the intervening space. 

6. Simultaneous Production of both Electrical States. 
— Neither kind of electrification is produced alone ; 
there is always an equal quantity of both kinds pro- 
duced ; one kind appearing on the thing rubbed and an 
equal amount of the other kind on the rubber. The 
clearest proof that these amounts are equal can be given 
in some cases. For it is found that if both the — electricity 
of the rubber and the + electricity of the thing rubbed be 
imparted to a third bod}^, that third body will show no 
electriji cation at all, the two equal and opposite electrifica- 
tions having exactly neutralized each other. A simple 



CHAP. I THEOEIES OF ELECTRICITY 9 

experiment consists in rubbing together a disk of sealing- 
wax and one covered with flannel, both being held by 
insulating handles. To test them is required an insulated 
pot and an electroscope, as in Fig. 29. If either disk be 
inserted in the pot the leaves of the electroscope will 
diverge ; but if both are inserted at the same time the 
leaves do not diverge, showing that the two charges on 
the disks are equal and of opposite sign. 

In the following list the bodies are arranged in such an 
order that if any two be rubbed together the one which 
stands earlier in the series becomes positively electrified, 
and the one that stands later negatively electrified : — 
Fw\ ivool, ivory, glass, silk, metals, sulphur, indiaruhher, 
guttapercha, collodion, or celluloid. 

7. Theories of Electricity. — Several theories have 
been advanced to account for these phenomena, but all 
are more or less unsatisfactory. Symmer proposed a 
"two-fluid" theory, according to which there are two 
imponderable electric fluids of opposite kinds, which 
neutralize one another when they combine, and which 
exist combined in equal quantities in all bodies until 
their condition is disturbed by friction. A modification 
of this theory was made by Franklin, who proposed 
instead a " one-fluid " theory, according to which there 
is a single electric fluid distributed usually uniformly 
in all bodies, but which, when they are subjected to 
friction, distributes itself unequally between the rubber 
and the thing rubbed, one having more of the fluid, the 
other less, than the average. Hence the terms positive 
and negative, which are still retained ; that body which is 
supposed to have an excess being said to be charged with 
positive electricity (usually denoted by \.h.Q plus sign +), 
while that which is supposed to have less is said to be 
charged with negative electricity (and is denoted by 
the minus sign — ). These terms are, how^ever, purely 
arbitrary, for in the present state of science we do not 
know which of these two states really means more and 



10 ELECTRICITY AND MAGNETISM part i 

which means less. In many ways electricity behaves as 
a weightless substance as incompressible as any material 
liquid. It is, however, quite certain that electricity is not 
a material Jiuid, whatever else it may be. For while it 
resembles a fluid in its property of apparently flowing 
from one point to another, it differs from every known 
fluid in almost every other respect. It possesses no 
weight ; it repels itself. It is, moreover, quite impossible 
to conceive of two fluids whose properties should in every 
respect be the precise opposites of one another. For 
these reasons it is clearly misleading to speak of an 
electric fluid or fluids, however convenient the term may 
seem to be. In metals and other good conductors elec- 
tricity can apparently move and flow quite easily in 
currents. In transparent solids, such as glass and resin, 
and in many transparent liquids such as oils, and in 
gases such as the air (if still, and not rarefied) electricity 
apparently cannot flow. Even a vacuum appears to be a 
non-conductor. In the case of all non-conductors elec- 
tricity can only be moved by an action known as displace- 
ment (see Art. .57). 

It appears then that in metals electricity can easily 
pass from molecule to molecule ; but in the case of non- 
conductors the electricity is in some way stuck to the 
molecules, or associated with them. Some electricians, 
notably Faraday, have propounded a molecular theory 
of electricity, according to which the electrical states are 
the result of certain peculiar conditions of the molecules 
of the surfaces that have been rubbed. Another view is 
to regard the state of electrification as related to the ether 
(the highly-attenuated medium which fills all space, and 
is the vehicle by which light is transmitted), which is 
known to be associated with the molecules of matter. 
Some indeed hold that the ether itself is electricity ; and 
that the two states of positive and negative electrifica- 
tion are simply due to displacement of the ether at the 
surfaces of bodies. In these lessons we shall avoid as 



ELECTRIC CHAEGES 



11 



far as possible all theories, and shall be content to use 
the term electricity. 

8. Charge. — The quantity of electrification of either 
kind produced by friction or other means upon the surface 
of a body is spoken of as a charge, and a body when 
electrified is said to be charged. It is clear that there 
may be charges of different values as well as of either 
kind. When the charge of electricity is removed from 
a charged body it is said to be discharged. Good con- 
ductors of electricity are instantaneously discharged if 
touched by the hand or by any conductor in contact with 
the ground,. the charge thus finding a means of escaping 
to earth or to surrounding walls. A body that is not a 
good conductor may be readily discharged by passing it 
rapidly through the flame of a spirit-lamp or a candle ; 
for the hot gases instantly carry off the charge and dis- 
sipate it in the air. 

Electricity may either reside upon the surface of bodies 
as a charge, or flow through their substance as a current. 
That branch of the science which treats of the laws of the 
charges, that is to say, of electricity at rest, upon the 
surface of bodies is termed electrostatics, and is dealt 
with in Chapter IV. The branch of the subject which 
treats of the flow of electricity in currents is dealt with 
in Chapter III., and other later portions of this book. 

9. Modes of representing Electrification. — Several 
modes are used to represent the electrification of surfaces. 
In Figs. 6, 7, and 8 are rep- 



B 



A B 



resented two disks — A cov- 
ered with woollen cloth, B 
of some resinous body, — 
which have been rubbed to- 
gether so that A has become 
positively, B negatively elec- 
trified. In Fig. 6 the sur- 
faces are marked with plus ( + ) and minus ( 



A_B 



U IT n 



Fiff. 6. 



Fig. 8. 

) signs. 



In Fig. 7 dotted lines are drawn just outside the posi- 



12 ELECTRICITY AND MAGNETISM part i 

tively electrified surface and just within the negatively 
electrified surface, as though one had a surplus and the 
other a deficit of electricity. In Fig. 8 lines are drawn 
across the intervening space from the positively electrified 
surface to the opposite negative charge. The advantages 
of this last mode are explained in Art. 13. 

10. Conductors and Insulators. — The term "con- 
ductors," used above, is applied to those bodies which 
readily allow electricity to flow through them. Roughly 
speaking, bodies may be divided into two classes — those 
which conduct and those which do not; though very 
many substances are partial conductors, and cannot well 
be classed in either category. All the metals conduct 
well ; the human body conducts, and so does water. On 
the other hand glass, sealing-wax, silk, shellac, gutta- 
percha, indiarubber, resin, fatty substances generally, 
and the air, are non-conductors. On this account these 
substances are used to make supports and handles for 
electrical apparatus where it is important that the elec- 
tricity should not leak away ; hence they are sometimes 
called insulators or isolators. Faraday termed them dielec- 
trics. We have remarked above that the name of non- 
electrics was given to those substances which, like the 
metals, yield no sign of electrification when held in the 
hand and rubbed. We now know the reason why they 
show^ no electrification; for, being good conductors, the 
electrification flows away as fast as it is generated. The 
observation of Gilbert that electrical experiments fail 
in damp weather is also explained by the knowledge that 
water is a conductor, the film of moisture on the surface 
of damp bodies causing the electricity produced by friction 
to leak away as fast as it is generated. 

11. Other Electrical Effects. — The production of elec- 
tricitj^ by friction is attested by other effects than those 
of attraction and repulsion, which hitherto we have 
assumed to be the test of the presence of electricity. 
Otto von Guericke first observed that sparks and flashes 



CHAP. I SOURCES OF ELECTRIFICATION 13 

of light could be obtained from highly electrified bodies 
at the moment \Yhen they were discharged. Such sparks 
are usually accompanied by a snapping sound, suggesting 
on a small scale the thunder accompanying the lightning 
spark, as was remarked by Newton and other early 
observers. Pale flashes of light are also produced by the 
discharge of electricity through tubes partially exhausted 
of air by the air-pump. Other effects will be noticed in 
due course. 

12. Other Sources of Electrification. — The student 
must be reminded that friction is by no means the only 
source of electrification. The other sources, percussion, 
compression, heat, chemical action, physiological action, 
contact of metals, etc., will be treated of in Lesson VII. 
We will simply remark here that friction between two 
different substances always produces electrical separa- 
tion, no matter what the substances may be. Symmer 
observed the production of electrification when a silk 
stocking was drawn over a woollen one, though woollen 
rubbed upon woollen, or silk rubbed upon silk, produces 
no electrical effect. If, however, a piece of rough glass 
be rubbed on a piece of smooth glass, electrification is 
observed ; and indeed the conditions of the surface play 
a very important part in the production of electrification 
by friction. In general, of two bodies thus rubbed 
together, that one becomes negatively electrical whose 
particles are the more easily removed by friction. Differ- 
ences of temperature also affect the electrical conditions 
of bodies, a warm body being usually negative when 
rubbed on a cold piece of the same substance. The 
quantity of electrification produced is, however, not pro- 
portional to the amount of the actual mechanical friction ; 
hence it appears doubtful whether friction is truly the 
cause of the electrification. Something certainly happens 
when the surfaces of two different substances are brought 
into intimate contact, which has the result that when 
they are drawn apart they are found (provided at least 



14 ELECTRICITY AXD :\rAGXETISM part i 

one of them is a non-conductor) to have acquired opposite 
charges of electrification; one surface having apparently 
taken some electricity from the other. But these opposite 
charges attract one another and cannot be drawn apart 
without there being mechanical work done upon the 
system. The work thus spent is stored up in the act 
of separating the charged surfaces; and as long as 
the charges remain separated they constitute a store 
of potential energy. The so-called frictional electric 
machines are therefore machines for bringing dissimilar 
substances into intimate contact, and then drawing apart 
the particles that have touched one another and become 
electrical. 

If the two bodies that are rubbed together are both 
good conductors, they will not become strongly electrified, 
even^if held on insulating handles. It is quite likely, 
however, that the heat produced by friction, as in the 
bearings of machinery, is due to electric currents gen- 
erated where the surfaces meet and slip. 

13. Electric Field. — Whenever two oppositely 
charged surfaces are placed near one another they tend 
to move together, and the space between them is found 
to be thrown into a peculiar state of 
stress, as though the medium in between 
had been stretched. To explore the 
space between two bodies one of which 
has been positively and the other nega- 
""■ ■ tively electrified, we may use a light 

pointer (Fig. 9) made of a smaU piece of very thin paper 
pierced with a hole through which passes a long thread 
of glass. It will be found that this pointer tends to 
point across from the positively electrified surface to 
the negatively electrified surface, along invisible lines of 
electric force. The space so filled with electric lines of 
force is called an electric field. In Fig. 8 A and B 
represent two bodies the surfaces of which have been 
electrified, the one positively, the other negatively. In 




ELECTROSCOPES 



15 



the field bet%Yeen them the electric lines pass across 

almost straight, except near the edges, where they are 

curved. Electric lines of force start from a positively 

charged surface at one end, and 

end on a negatively charged 

surface at the other end. They 

never meet or cross one another. 

Their direction indicates that of 

the resultant electric force at 

every point through which they 

pass. The stress in the medium 

thus mapped out by the lines of 

force acts as a tension along 

them, as though they tended to 

shorten themselves. In fact in Fig. 8 the tension in the 

medium draws the two surfaces together. There is also 

a pressure in the medium at right angles to the lines, 

tending to widen the distance between them. Fig. 10 

represents a ball which has been positively electrified, 

and placed at a distance from other objects; the lines in 

the field being simply radial. 




Fig. 10. 



Lesson II. — Electroscopes 

14. Simple Electroscopes. — An instrument for detect- 
ing whether a body is electrified or not, and whether 
the electrification is positive or negative, is termed an 
Electroscope. The feather which was attracted or re- 
pelled, and the two pith-balls which flew apart, as we 
found in Lesson I., are in reality simple electroscopes. 
There are, however, a number of pieces of apparatus 
better adapted for this particular purpose, some of which 
we will describe. 

15. Needle Electroscope. — The earliest electroscope 
was that devised by Dr. Gilbert, and shown in Fig. 11, 
which consists of a stiff strip balanced lightly upon a 
sharp point. A thin strip of brass or wood, a straw, or 



16 



ELECTHICITY AND MAGNETISM part i 



even a goose quill, balanced upon a sewing needle, will 
serve equally well. When an electrified body is held near 




Fig. 11. 



the electroscope it is attracted and turned round, and will 
thus indicate the presence of electric charges far too feeble 
to attract bits of paper from a table. 

16. Gold-Leaf Electroscope. — A still more sensi- 




Fia. 1-j 



tive instrument is the Gold-Leaf Electroscope, invented 
by Bennet, and shown in Fig. 12. We have seen 
how two pith-balls when similarly electrified repel one 



CHAP. I GOLD-LEAF ELECTROSCOPE 17 

another and stand apart, gravity being partly overcome 
by the force of the electric repulsion. A couple of 
narrow strips of the thinnest tissue paper, hung upon a 
support, will behave similarly when electrified. But the 
best results are obtained with two strips of gold leaf, 
which, being excessively thin, is much lighter than the 
thinnest paper. The Gold -Leaf Electroscope is con- 
veniently made by suspending the two leaves within a 
wide-mouthed glass jar, which both serves to protect 
them from draughts of air and to support them from 
contact with the ground. The mouth of the jar should 
be closed by a plug of paraffin wax, through which is 
pushed a bit of varnished glass tube. Through this 
passes a stiff brass wire, the lower end of which is bent 
at a right angle to receive the two strips of gold leaf, 
while the upper supports a flat plate of metal, or may be 
furnished with a brass knob. When kept dry and free 
from dust it will indicate excessively small quantities of 
electrification. A rubbed glass rod, even while two or 
three feet from the instrument, will cause the leaves to 
repel one another. The chips produced by sharpening a 
pencil, falling on the electroscope top, are seen to be 
electrified. If the knob be even brushed with a small 
camel's hair brush, the slight friction produces a percep- 
tible effect. With this instrument all kinds of friction 
can be shown to produce electrification. Let a person, 
standing upon an insulating support, — such as a stool 
with glass legs, or a board supported on four glass 
tumblers, — be briskly struck with a silk handkerchief, 
or with a fox's tail, or even brushed with a clothes brush, 
he will be electrified, as will be indicated by the electro- 
scope if he place one hand on the knob at the top of it. 
The Gold-Leaf Electroscope can further be used to indi- 
cate the kind of electrification on an excited body. Thus, 
suppose we rubbed a piece of brown paper with a piece of 
indiarubber and desired to find out whether the electri- 
fication excited on the paper was + or — , we should 
c 



18 



ELECTRICITY AND MAGXETISM pakt i 



proceed as follows : — First charge the gold leaves of the 
electroscope by touching the knob with a glass rod rubbed 
on silk. The leaves diverge, being electrified with + 
electrification. When they are thus charged the approach 
of a body which is positively electrified will cause them 
to diverge still more widely ; while, on the approach of 
one negatively electrified, they will tend to close together. 
If now the brown paper be brought near the electroscope, 
the leaves will be seen to diverge more, proving the 
electrification of the paper to be of the same kind as 
that with which the electroscope is charged, or positive. 

Sometimes the outer surface 
of the glass jar containing 
the gold leaves is covered 
with wire gauze or strips of 
foil to shield the leaves from 
the influence of external 
bodies. A preferable way is 
to use glass of a kind that 
conducts. 

The part plaj'ed by the 
surrounding medium in the 
operation of the electroscope 
is illustrated by Fig. 13. 
Of the electric lines in the 
field surrounding the rubbed rod a number will pass into 
the metal cap of the electroscope and emerge below 
through the leaves. The nearer the rod is brought, the 
greater will be the number of electric lines thus affecting 
the instrument. There being a tension along the lines 
and a pressure across them, the effect is to draw the gold 
leaves apart as though they repelled each other. 

The Gold-Leaf Electroscope will also indicate roughly 
the amount of electrification on a body placed in contact 
with it, for the gold leaves open out more widely when 
the charge thus imparted to them is greater. For exact 
measurement, however, of the degree of electrification. 




Fig. 13. 



ELECTEOSCOPE 



X 



19 



recourse must be had to the instruments known as 
Electrometers, described in Lesson XXII. 

In another form of electroscope (Bohnenberger's) a 
single gold leaf is used, and is suspended between two 
metallic plates, one of which can be positively, the other 
negatively electrified, by placing them in communication 
with the poles of a " dry pile " (Art. 193). If the gold 
leaf be charged positively or negatively it will be attracted 
to one side and repelled from the other, according to the 
law of attraction and repulsion mentioned in Art. 4. 

\ 17. Henley's Semaphore. — As an indicator for large 
charges of electricity there is sometimes used a sema- 
phore like that shown in Fig. 14. 
It consists of a pith-ball at the end 
of a light arm fixed on a pivot to 
an upright. When the whole is 
electrified the pith-ball is repelled 
from the upright and flies out at an 
angle, indicated on a graduated 
scale or dial behind it. This little 
electroscope, which is seldom used 
except to show whether an electric 
machine or a Leyden battery is 
charged, must on no account be con- 
fused with the delicate " Quadrant 
Electrometer" described in Lesson 
XXIL, whose object is to measure very small charges of 
electricity — not to indicate large ones. 

18. The Torsion Balance. — Although more properly 




Fig. 14. 



an Electrometer than a mere Electros 



roscope, 



it will be 



most convenient to describe here the instrument known 
as the Torsion Balance (Fig. 15). This instrument, once 
famous, but now quite obsolete, served to measure the 
force of the repulsion between two similarly electrified 
bodies, by balancing the repelling force against the force 
exerted by a fine wire in untwisting itself after it has 
been twisted. The torsion balance consists of a light arm 



ELECTRICITY AND MAGNETISM paet i 



or lever of shellac suspended within a cylindrical glass 
case by means of a fine silver wire. At one end this 
lever is furnished with a gilt pith-ball n. The upper 
end of the silver wire is fastened to a brass top, upon 

which a circle, divided 
into degrees, is cut. This 
top can be turned round 
in the tube which sup- 
ports it, and is called the 
torsion-head. Through an 
aperture in the cover there 
can be introduced a sec- 
ond gilt pith-ball m, fixed 
to the end of a vertical 
glass rod a. Round the 
glass case, at the level of 
the pith-balls, a circle is 
drawn, and divided also 
into degrees. 

In using the torsion 
balance to measure the amount of a charge of electricity, 
the following method is adopted : — First, the torsion-head 
is turned round until the two pith-balls m and n just 
touch one another. Then the glass rod a is taken out, 
and the charge of electricity to be measured is imparted 
to the ball m, which is then replaced in the balance. As 
soon as m and n touch one another, part of the charge 
passes from m to n, and they repel one another because 
they are then similarly electrified. The ball n, therefore, 
is driven round and twists the wire up to a certain extent. 
The force of repulsion becomes less and less as n gets 
farther and farther from m; but the force of the twist 
gets greater and greater the more the wire is twisted. 
Hence these two forces will balance one another when 
the balls are separated by a certain distance, and it is 
clear that a large charge of electricity will repel the ball 
n with a greater force than a lesser charge would. The 




Fig. 15. 



CHAP. I LAW OE INVEKSE SQUARES 21 

distance through which the ball is repelled is read off in 
angular degrees of the scale. When a wire is twisted, 
the force with which it tends to untwist is precisely pro- 
portional to the amount of the twist. The force required 
to twist the wire ten degrees is just ten times as great 
as the force required to twist it one degree. In other 
words, the force of torsion is proportional to the angle of 
torsion. The angular distance between the two balls is, 
when they are not very widely separated, very nearly 
proportional to the actual straight distance between them, 
and represents the force exerted between electrified balls 
at that distance apart. The student must, however, care- 
fully distinguish between the measurement of the force 
and the measurement of the actual quantity of electricity 
with W'hich the instrument is charged. For the force 
exerted between the electrified balls will vary at different 
distances according to a particular law known as the 
" law of inverse squares," which requires to be carefully 
explained. 

19. The Law of Inverse Squares. — Coulomb proved, 
by means of the Torsion Balance, that the force exerted 
between two small electrifi.ed bodies varies inversely as 
the square of the distance between them when the 
distance is varied. Thus, suppose two small electrified 
bodies 1 inch apart repel one another with a certain 
force, at a distance of 2 inches the force will be found 
to be only one quarter as great as the force at 1 inch ; 
and at 10 inches it will be only y^o part as great as 
at 1 inch. This law is proved by the following ex- 
periment with the torsion balance. The two scales were 
adjusted to 0°, and a certain charge was then imparted 
to the balls. The ball n was repelled round to a distance 
of 36°. The twist on the wire between its upper and 
lower ends was also 36° or the force tending to repel 
was thirty-six times as great as the force required to 
twist the wire by 1°. The torsion-head was now turned 
round so as to twist the thread at the top and force 



22 ELECTRICITY AND MAGNETISM part i 

the ball n nearer to m, and was turned round until 
the distance between n and 711 was halved. To brmg 
down this distance from 36° to 18°, it was found 
needful to twist the torsion-head through 126°. The 
total twist between the upper and lower ends of the 
wire was now 126°+ 18°, or 144°; and the force was 
144 times as great as that force which would twist 
the wire 1°. But 144 is four times as great as 36 ; 
hence w-e see that while the distance had been reduced 
to one Jialf, the force between the balls had become 
fow^ times as great. Had we reduced the distance 
to one quarter, or 9°, the total torsion would have been 
found to be 576°, or sixteen times as great ; proving 
the force to vary inversely as the square of the dis- 
tance. 

In practice it requires great experience and skill to 
obtain results as exact as this, for there are many sources 
of inaccuracy in the instrument. The balls must be very 
small, in proportion to the distances betw^een them. The 
charges of electricity on the balls are found, moreover, to 
become gradually less and less, as if the electricity leaked 
away into the air. This loss is less if the apparatus be 
quite dry. It is therefore usual to dry the interior by 
placing inside the case a cup containing either chloride 
of calcium, or pumice stone soaked with strong sulphuric 
acid, to absorb the moisture. 

Before leaving the subject of electric forces, it may be 
well to mention that the force of attraction between two 
oppositely electrified bodies varies also inversely as the 
square of the distance between them. And in every 
case, whether of attraction or repulsion, the force at any 
given distance is proportional to the product of the two 
quantities of electricity on the bodies. Thus, if we 
had separately given a charge of 2 to the ball m and a 
charge of 3 to the ball n, the force between them will be 
3x2 = 6 times as great as if each had had a charge of 1 
given to it. It must be remembered, however, that the 



CHAP. I ELECTRIC EIELD 23 

law of inverse squares is only true when applied to the 
case of bodies so small, as compared with the distance 
between them, that they are mere points. For flat, large, 
or elongated bodies the law of inverse squares does not 
hold good. The attraction between two large flat disks 
oppositely electrified with given charges, and placed near 
together, does not vary with the distance. 

20. Field between two Balls. — The electric field 
(Art. 13) between two oppositely electrified balls is found 
to consist of curved lines. 
By the principle laid down 
in Art. 13, there is a tension 
along these lines so that 
they tend not only to draw 
the two balls together, but 
also to draw the electrifica- 
tions on the surfaces of the 
balls toward one another. 
There is also a lateral pressure in the medium tending to 
keep the electric lines apart from one another. One 
result of these actions is that the charges are no longer 
equally distributed over the surfaces, but are more dense 
on the parts that approach most nearly. 

21. Unit Quantity of Electricity. — In consequence of 
these laws of attraction and repulsion, it is found most 
convenient to adopt the following definition for that 
quantity of electricity which we take for a unit or stand- 
ard by which to measure other quantities of electricity. 
One {electrostatic) Unit of Electricity is that quantity ivhich, 
when placed at a distance of one centimetre in air from 
a similar and equal quantity, repels it with a force of one 
dyne. If instead of air another medium occupies the 
space, the force will be different. For example, if petro- 
leum is used the force exerted between given charges 
will be about half as great (see Art. 56). Further in- 
formation about the measurement of electrical quantities 
is given in Lessons XXL and XXII. 




24 



ELECTRICITY AXD IVIAGNETISM part i 



Lesson III. — Electrification by Injluence 

22. Influence. — We have now learned how two 
charged bodies may apparently attract or repel one 
another. It is sometimes said that it is the charges in 
the bodies which attract or repel one another; but as 
electrification is not known to exist except in or on 
material bodies, the proof that it is the charges them- 
selves which are acted upon is only indirect. Xevertheless 
there are certain matters which support this view, one of 




Fig. IT. 



these being the electric influence exerted by an electrified 
body upon one not electrified. 

Suppose we electrify positively a ball C, shown in Fig. 
17, and hold it near to a body that has not been electri- 
fied, what will occur? We take for this experiment the 
apparatus shown on the right, consisting of a long sausage- 
shaped piece of metal, either hollow or solid, held upon a 
glass support. This •• conductor," so called because it is 
made of metal which permits electricity to pass freely 
through it or over its surface, is supported on glass to 



INFLUENCE 25 



prevent the escape of electricity to the earth, glass being 
a non-conductor. The influence of the positive charge 
of the ball placed near this conductor is found to induce 
electrification on the conductor, which, although it has 
not been rubbed itself, will be found to behave at its two 
ends as an electrified body. The ends of the conductor 
will attract little bits of paper ; and if pith-balls be hung 
to the ends they are found to be repelled. It will, how- 
ever, be found that the middle region of the long-shaped 
conductor will give no sign of any electrification. Further 
examination will show that the two electrifications on the 
ends of the conductor are of opposite kinds, that nearest 
the excited glass ball being a negative charge, and that at 
the farthest end being an equal charge, but of positive 
sign. It appears then that a positive charge attracts 
negative and repels positive, and that this influence can 
be exerted at a distance from a body. If we had begun 
with a charge of negative electrification upon a stick of 
sealing-wax, the presence of the negative charge near the 
conductor would have induced a positive charge on the 
near end, and negative on the far end. This action, 
discovered in 1753 by John Canton, is spoken of as 
influence or electrostatic induction.* It will take 
place across a considerable distance. Even if a large 
sheet of glass be placed between, the same effect will be 
produced. When the electrified body is removed both 
the charges disappear and leave no trace behind, and 
the glass ball is found to be just as much electrified as 
before ; it has parted with none of its own charge. It 



* The word induction originally used was intended to denote an action 
at a distance, as distinguished from conduction, which implied the convey- 
ance of the action by a material conductor. But there were discovered 
other actions at a distance, namely, the induction of currents by moving 
magnets, or by other currents, and the induction of magnetism in iron in 
the presence of a neighbouring magnet. As the term induction has now 
been officially adopted for the induction of currents, its use in other senses 
ought to be dropped. Hence the preference now given to the term influ- 
ence for the Induction of charges by charges. 



26 



ELECTRICITY AXD MAGNETISM part i 



will be remembered that on oue theory a body charged 
positively is regarded as having more electricity than 
the things round it, while one with a negative charge is 
regarded as having less. According to this view it would 
appear that when a body (such as the -f electrified glass 
ball) having more electricity than things around it is 
placed near an insulated conductor, the uniform distribu- 
tion of electricity in that conductor is disturbed, the 
electricity flowing away from that end which is near the 
-f body, leaving less than usual at that end, and producing 

more than usual at the other 
end. This view of things will 
account for the disappear- 
ance of all signs of electrifi- 
cation when the electrified 
body is removed, for then 
the conductor returns to its 
former condition ; and being 
neither more nor less elec- 
trified than ail the objects 
around on the surface of the 
earth, will show neither positive nor negative charge. 
The action is not, however, a mere action at a distance; 
it is one in which the intervening medium takes- an essen- 
tial part. Consider (Fig. 18) what takes i^lace when an 
insulated, non-electrified metal baU B is brought under 
the influence of a positively electrified body A. At 
once some of the electric lines of the field that surrounds 
A pass through B, entering it at the side nearer A, and 
leaving it at the farther side. As the ball B has no 
charge of its own, as many electric lines will enter on one 
side as leave on the other; or, in other words, the induced 
negative charge on one side and the induced positive 
charge on the other will be exactly equal in amount. 
They will not, however, be quite equally distributed, the 
negative charge on the side nearer A being more concen- 
trated, and the lines in the field on that side denser. 




CHAP. I ELECTRIC INFLUENCE 27 

23. Effects of Influence. — If the conductor be made 
ill two parts, which while under the influence of the 
electrified body are separated, then on the removal of the 
electrified body the two charges can no longer return to 
neutralize one another, but remain each on its own 
portion of the conductor. 

If the conductor be not insulated on glass supports, 
but placed in contact wdth the ground, that end only 
which is nearest the electrified body will be found to 
be electrified. The repelled charge is indeed repelled as 
far as possible into the walls of the room ; or, if the 
experiment be performed in the open air, into the earth. 
One kind of electrification only is under these circum- 
stances to be found, namely, the opposite kind to that 
of the excited body, whichever this may be. The same 
effect occurs in this case as if an electrified body had the 
power of attracting up the opposite kind of charge out of 
the earth. 

The quantity of the two charges thus separated by 
influence on such a conductor in the presence of a charge 
of electricity, depends upon the amount of the charge, 
and upon the distance of the charged body from the 
conductor. A highly electrified glass rod will exert a 
greater influence than a less highly electrified one ; and 
it produces a greater effect as it is brought nearer and 
nearer. The utmost it can do will be to induce on the 
near end a negative charge equal in amount to its own 
positive charge, and a similar amount of positive electri- 
fication at the far end ; but usually, before the electrified 
body can be brought so near as to do this, something else 
occurs which entirely alters the condition of things. As 
the electrified body is brought nearer and nearer, the 
charges of opposite sign on the two opposed surfaces 
attract one another more and more strongly and accumu- 
late more and more densely, until, as the electrified body 
approaches very near, a spark is seen to dart across, the 
two charges thus rushing together to neutralize one 



28 



ELECTRICITY AND MAGNETISM part i 




another, leaving the induced charge of positive electricity, 
which was formerly repelled to the other end of the 
conductor, as a permanent charge after the electrified 
body has been removed. 

In Fig. 19 is illustrated the operation of gradually 
lowering down over a table a positively electrified njetal 
ball. The nearer it approaches the table, the more does 
the electric field surrounding it concentrate itself in the 
gap between the ball and the 
table top; the latter becoming 
negatively electrified by influ- 
ence. Where the electric lines 
are densest the tension in the 
medium is greatest, until when 
the ball is lowered still further 
the mechanical resistance of the 
air can no longer withstand 
the stress; it breaks down and 
the layer of air is pierced by a 
spark. If oil is used as a surrounding medium instead of 
air, it will be found to stand a much greater stress without 
being pierced. 

24. Attraction due to Influence. — We are now able 
to apply the principle of influence to explain why an 
electrified body should attract things that have not been 
electrified at all. Fig. 18, on p. 26, may be taken to 
represent a light metal ball B hung from a silk thread 
presented to the end of a rubbed glass rod A. The 
positive charge on A produces hy injiuence a negative 
charge on the nearer side of B and an equal positive 
charge on the far side of B. The nearer half of the ball 
will therefore be attracted, and the farther half repelled ; 
but the attraction will be stronger than the repulsion, 
because the attracted charge is nearer than the repelled. 
Hence on the whole the ball will be attracted. It can 
easily be observed that if a ball of non-conducting 
substance, such as wax, be employed, it is not attracted 



Fig. 19. 



CHAP. I THE ELECTROPHOKUS 29 

so much as a ball of conducting material. This in itself 
proces that inflaence really precedes attraction. 

Another way of stating the facts is as follows : — The 
tension along the electric field on the right of B will be 
greater than that on the left, because of the greater 
concentration of the electric lines on the right. 

25. Dielectric Power. — We have pointed out several 
times what part the intervening medium plays in these 
actions at a distance. The air, oil, glass, or other material 
between does not act simply as a non-conductor; it takes 
part in the propagation of the electric forces. Hence 
Faraday, who discovered this fact, termed such materials 
dielectrics. Had oil, or solid sulphur, or glass been used 
instead of air, the influence exerted by the presence of the 
electrified body at the same distance would have been 
greater. The power of a non-conducting substance to 
convey the influence of an electrified body across it is 
called its dielectric power (or was formerly called its 
specific inductive capacity, see Art. 56 and Lesson XXIH.). 

26. The Electrophorus. — We are now prepared to 
explain the operation of a simple and ingenious instru- 
ment, devised by Volta in 1775, for the purpose of 
procuring, by the principle of influence, an unlimited 
number of charges of electricity from one single charge. 
This instrument* is the Electrophorus (Fig. 20). It 
consists of two parts, a round cake of resinous material 
cast in a metal dish or "sole," about 12 inches in 
diameter, and a round disk of slightly smaller diameter 
made of metal, or of wood covered with tinfoil, and 
provided with a glass handle. Shellac, or sealing-wax, or 
a mixture of resin, shellac, and Venice turpentine, may 
be used to make the cake. A slab of sulphur will also 
answer, but it is liable to crack. Sheets of hard ebonized 
indiarubber are excellent ; but the surface of this substance 

* Volta' s electrophorus was announced in 1775. Its principle had 
already been anticipated by Wilcke, who in 1762 described to the Swedish 
Academy of Sciences two " charging-machines " working by influence. 



30 



ELECTRICITY AND MAGNETISM part i 



requires occasional washing with ammonia and rubbing- 
with paraffin oil, as the sulphur contained in it is liable 
to oxidize and to attract moisture. To use the electro- 
phorus the resinous cake must be beaten or rubbed with 
a warm piece of woollen cloth, or, better still, with a cat's 




skin. The disk or " cover " is then placed upon the cake, 
touched momentarily with the finger, then removed by- 
taking it up by the glass handle, when it is found to be 
powerfully electrified with a positive charge, so much so 
indeed as to yield a spark when the knuckle is presented 
to it. The " cover " may be replaced, touched, and once 
more removed, and will thus yield any number of sparks, 



CHAP. I THE ELECTROPHORUS 31 

the original charge, on the resinous plate meanwhile 
remaining practically as strong as before. 

The theory of the electrophorus is very simple, pro- 
vided the student has clearly grasped the principle of 
influence explained above. When the resinous cake is 
first beaten with the cat's skin its surface is negatively 
electrified, as indicated in Fig. 21. When the metal disk 
is placed down upon it, it rests really only on three or 
four points of the surface, and may be regarded as an 
insulated conductor in the presence of an electrified body. 
The negative electrification of the cake therefore acts by 
influence on the metallic disk or " cover," the natural 
electricity in it being displaced downwards, producing a 
positive charge on the under side, and leaving the upper 



>\\liij//^ 



Fig. 21. Fig. 22. 

side negatively electrified. This state of things is shown 
in Fig. 22. If now the cover be touched for an instant 
with the finger, the negative charge of the upper surface 
will be neutralized by electricity flowing in from the earth 
through the hand and body of the experimenter. The 
attracted positive charge will, however, remain, being 
bound as it were by its attraction towards the negative 
charge on the cake. Fig. 23 shows the condition of 
things after the cover has been touched. If, finally, the 
cover be lifted by its handle, the remaining positive 
charge will be no longer "bound" on the lower surface 
by attraction, but will distribute itself on both sides of 
the cover, and may be used to give a spark, as already 
said. It is clear that no part of the original charge has 
been consumed in the process, which may be repeated as 



32 



ELECTRICITY AND MAGNETISM part i 



often as desired. As a matter of fajst, the charge on the 
cake slowly dissipates — especiall}^ if the air be damp. 
Hence it is needful sometimes to renew the original charge 
by afresh beating the cake with the cat's skin. The 
labour of touching the cover with the finger at each 
operation may be saved by having a pin of brass or a 
strip of tinfoil projecting from the metallic '• sole " on to 
the top of the cake, so that it touches the plate each time, 
and thus neutralizes the negative charge by allowing 
electricity to flow in from the earth. 

The principle of the electrophorus may then be 
summed up in the following sentence. A conductor if 



i;^. 



Fig. 23. 




I t-^-f^T^T^n 



Fig. 24. 



touched while under the influence of a charged body acquires 
thereby a charge of opposite sign.* 

Since the electricity thus yielded by the electro- 
phorus is not obtained at the expense of any part of the 
original charge, it is a matter of some interest to inquire 
what the source is from which the energy of this apparently 
unlimited supply is drawn ; for it cannot be called into 



* Priestley, in 1T67, stated this principle in the follo\ving language : — 
" The electric fluid, -when there is a redundancy of it in any body, repels 
the electric fluid in any other body, when they are brought ^vithin the 
sphere of each other's influence, and drives it into the remote parts of the 
body ; or quite out of the body, if there be any outlet for that purpose. 
In other words, bodies immerged in electric atmospheres always become 
possessed of the electricity, contrary to that of the body, in whose atmo- 
sphere they are immerged." 



CHAP. I FREE AND BOUND CHARGES 33 

existence without the expenditure of some other form of 
energy, any more than a steam-engine can work without 
fuel. As a matter of fact it is found that it is a little 
harder work to lift up the cover when it is charged than 
if it were not charged ; for, when charged, there is the . 
tension of the electric field to be overcome as well as the 
force of gi'avity. Slightly harder work is done at the ex- 
pense of the muscular energies of the operator ; and this 
is the real origin of the energy stored up in the separate 
charges. The purely mechanical actions of putting down 
the disk on the cake, touching it, and lifting it up, 
can be performed automatically by suitable mechanical 
arrangements, which render the production of these 
inductive charges practically continuous. Of such con- 
tinuous electrophori, the latest is Wimshurst's machine, 
described in Lesson Y. 

27. ''Free" and ''Bound" Electrification. — We 
have spoken of a charge of electricity on the surface of a 
conductor, as being " bound " when it is attracted by the 
presence of a neighbouring charge of the opposite kind. 
The converse term " free " is sometimes applied to the 
ordinary state of electricity upon a charged conductor, 
not in the presence of a charge of an opposite kind. A 
"free" charge upon an insulated conductor flows away 
instantaneously to the earth, if a conducting channel be 
provided, as will be explained. It is immaterial what 
point of the conductor be touched. Thus, in the case 
represented in Fig. 17, wherein a -f electrified body 
induces — electrification at the near end, and -f electri- 
fication at the far end of an insulated conductor, the — 
charge is " bound," being attracted, while the + charge 
at the other end, being repelled, is " free " ; and if the 
insulated conductor be touched by a person standing on the 
ground, the "free" charge will flow away through his body 
to the earth, or to the walls of the room, while the "bound " 
charge will remain, no matter whether he touch the con- 
ductor at the far end, or at the near end, or at the middle, 
n 



34 ELECTPJCnr AND MAGNETISM pakt i 

28. Method of charging the Gold-Leaf Electroscope 
by Influence. — The student will now be prepared to 
understand the method by vrliich a Gold-Leaf Electro- 
scope can be charged with the opposite kind of charge to 
that of the electrified body used to charge it. Tu Lesson 
IL it was assumed that the way to charge an electroscope 
was to place the excited body in contact with the knob, 
and thus permit, as it were, a small portion of the charge 
to flow into the gold leaves. A rod of glass rubbed on 
silk being 4- would thus obviously impart -f electrifica- 
tion to the gold leaves. 

Suppose, however, the rubbed glass rod to be held a 
few inches above the knob of the electroscope, as is 
indeed shown in Fig. 12. Even at this distance the gold 
leaves diverge, and the effect is due to influence. The 
gold leaves, and the brass wire and knob, form one con- 
tinuous conductor, insulated from the ground by the 
glass jar. The presence of the -f charge of the glass acts 
inductively on this "insulated conductor," inducing — 
electrification on the near end or knob, and inducing -f 
at the far end, i.e. on the gold leaves, which diverge. 
Of these two induced charges, the — on the knob is 
'• bound," while the -f on the leaves is " free." If now, 
while the excited rod is still held above the electroscope, 
the knob be touched by a person standing on the ground, 
one of these two induced charges flows to the ground, 
namely, the free charge — not that on the knob itself, for 
it was "bound," but that on the gold leaves which was 
"free" — and the gold leaves instantly drop down straight. 
There now remains only the — charge on the knob, 
" bound " so long as the -f charge of the glass rod is 
near to attract it. But if, finally, the glass rod be taken 
right away, the — charge is no longer "bound" on the 
knob, but is " free " to flow into the leaves, which once 
more diverge — but this time with a negative electrification. 

29. The "Return-Shock." — It is sometimes noticed 
that, when a charged conductor is suddenly discharged, 



CONDUCTIOX 35 



a discharge is felt by persons standing near, or may 
even affect electroscopes, or yield sparks. This action, 
known as the "return-shock," is due to influence. For 
in the presence of a charged conductor a charge of 
opposite sign will be induced in neighbouring bodies, 
and on the discharge of the conductor these neighbour- 
ing bodies may also suddenly discharge their induced 
charge into the earth, or into other conducting bodies. 
A "return-shock" is sometimes felt by persons standing 
on the gTound at the moment when a flash of lightning- 
has struck an object some distance away. 



Lessox TV. — Conduction and Distribution of Electricity 

30. Conduction. — Toward the close of Lesson I. we 
explained how certain bodies, such as the metals, conduct 
electricity, while others are non-conductors or insulators. 
This discovery is due to Stephen Gray ; who, in 1729, 
found that a cork, inserted into the end of a rubbed glass 
tube, and even a rod of wood stuck into the cork, pos- 
sessed the power of attracting light bodies. He found, 
similarly, that metallic wire and pack-thread conducted 
electricity, while silk did not. 

We may repeat these experiments by taking (as in 
Fig. 25) a glass rod, fitted with a cork and a piece of 
wood. If a bullet or a brass knob be hung to the end of 
this by a linen thread or a wire, it is found that when the 
glass tube is rubbed the bullet acquires the property of 
attracting light bodies. If a dry silk thread is used, 
however, no electricity will flow down to the bullet. 

Gray even succeeded in transmitting a charge of 
electricity through a hempen thread over 700 feet long, 
suspended on silken loops. A little later Du Fay 
succeeded in sending electricity to no less a distance 
than 1256 feet through a moistened thread, thus proving 
the conducting power of moisture. From that time the 



ELECTRICITY AND MAGNETISM part 



classification of bodies into conductors and insulators has 
been observed. 

This distinction cannot, however, be entirely main- 
tained, as a large class of substances occupy an inter- 
mediate ground as partial conductors. For example, dry 
wood is a bad conductor and also a bad insulator ; it 
is a good enough conductor to conduct away the high- 
potential electricity obtained by friction, but it is a 
bad conductor for the relatively low-potential electricity 
of small voltaic batteries. Substances that are very bad 





conductors are said to offer a great resistance to the 
flow of electricity through them. There is indeed no 
substance so good a conductor as to be devoid of resist- 
ance. There is no substance of so high a resistance as 
not to conduct a little. Even silver, which conducts best 
of all known substances, resists the flow of electricity to 
a small extent; and, on the other hand, such a non-con- 
ducting substance as glass, though its resistance is many 
million times greater than any metal, does allow a very 
small quantity of electricity to pass through it. In the 



CONDUCTORS 



37 



following list, the substances named are placed in order, 
each conductino' better than those lower down on the list. 



Silver . . 
Copper . . 
Other metals 


1 


j- Good Conductors. 


Charcoal . 


Water . . 


J 


The body . 


1 


Cotton . . 


1^ Partial Conductors 


Dry wood . 


Marble . . 


1 


Paper . . 


J 


Oils . . . 




Porcelain . 




Wool . . 




Silk . . . 




Resin . . 




Guttapercha 


, Non-Conductors or 


Shellac . . 


'' Insulators. 


Ebonite . 




Paraffin . 




Glass . . 




Quartz (fused 


) 


Air . . . 


J 



A simple way of observing experimentally whether a 
body is a conductor or not, is to take a charged gold- 
leaf electroscope, and, holding the substance to be 
examined in the hand, touch the knob of the electro- 
scope with it. If the substance is a conductor the elec- 
tricity will flow away through it and through the body 
to the earth, and the electroscope will be discharged. 
Through good conductors the rapidity of the flow is so 
great that the discharge is practically instantaneous. 
Further information on this question is given in Lesson 
XXXIII. 

31. Distribution of Charge on Bodies. — If electri- 
fication is pioduced at one part of a non-conducting 
body, it remains at that point and does not flow over 
the surface, or at most flows over it excessively slowly. 



38 ELECTRICITY AND MAGNETISM paht i 

Tims if a glass tube is rubbed at one end, only that one 
end is electrified. Hot glass is, however, a conductor. 
If a warm cake of resin be rubbed at one part with a 
piece of cloth, only the portion rubbed will attract light 
bodies, as may be proved by dusting upon it through 
a piece of muslin fine powders such as red lead, lyco- 
podium, or verdigris, which adhere where the surface is 
electrified. The case is, however, wholly different when 
a charge of electricity is imparted to any part of a con- 
ducting body placed on an insulating support, for it 
instantly distributes itself all over the surface, though in 
general not uniformly over all points of the surface. 

32. The Charge resides on the Surface. — A charge 
of electricity resides only on the surface of conducting 
bodies. This is proved by the fact that it is found 
to be immaterial to the distribution what the inte- 
rior of a conductor is made of; it may be solid metal, 
or hollow, or even consist of wood covered with tinfoil 
or gilt, but, if the shape be the same, the charge will 
distribute itself precisely in the same manner over the 
surface. There are also several Avays of proving by 
direct experiment this very important fact. Let a hollow 
metal ball, having an aperture at the top, be taken (as in 
Fig. 26), and set upon an insulating stem, and charged 
by sending into it a few sparks from an electrophorus. 
The absence of any charge in the interior may be shown 
as follows : — In order to observe the nature of the elec- 
trification of a charged body, it is convenient to have some 
means of removing a small quantity of the charge as 
a sample for examination. To obtain such a sample, a 
little instrument known as a proof-plane is employed. 
It consists of a little disk of sheet copper or of gilt paper 
fixed at the end of a small glass rod. If this disk is laid 
on the surface of an electrified body at any point, part 
of the charge flows into it, and it may be then removed, 
and the sample thus obtained may be examined with a 
gold-leaf electroscope in the ordinary way. For some 



CHARGE ON SURFACE 



39 



purposes a metallic bead, fastened to the end of a glass 
rod, is more convenient than a flat disk. If such a proof- 
plane be applied to the outside of our electrified hollow 
ball, and then touched on the knob of an electroscope, 
the gold leaves will diverge, showing the presence of a 




Fig. 26. 



charge. But if the proof-plane be carefully inserted 
through the opening, and touched against the inside of 
the globe and then withdrawn, it will be found that 
the inside is destitute of electrification. An electrified 
pewter mug will show a similar result, and so will even 
a cylinder of gauze wire. 



40 



ELECTEICITY AND MAGNETISM part 



33. Biot's Experiment. — Biot proved the same fact 
in another way. A copper ball was electrified and 
insulated. Two hollow hemispheres of copper, of a 
larger size, and furnished with glass handles, were then 
placed together outside it (Fig. 27). So long as they 
did not come into contact the charge remained on the 
inner sphere; but if the outer shell touched the inner 
sphere for but an instant, the whole of the charge passed 



A 




Fig. 27. 

to the exterior ; and when the hemispheres were separated 
and removed the inner globe was found to be completely 
discharged. 

34. Further Explanation. — Doubtless the explana- 
tion of this behaviour of electricity is to be found in the 
property previously noticed as possessed by either kind 
of electrification, namely, that of repelling itself ; hence 
it retreats as far as can be from the centre and remains 
upon the surface. An important proposition concerning 
the absence of electric force within a closed conductor is 
proved in Lesson XXI. ; meanwhile it must be noted that 
the proofs, so far, are directed to demonstrate the absence 



ELECTRIFICATION EXTERNAL 



41 



of a free charge of electricity in the interior of hollow con- 
ductors. Amongst other experiments, Terqueni showed 
that a pair of gold leaves hung inside a wire cage could 
not be made to diverge when the cage was electrified. 
Faraday constructed a conical bag of linen-gauze, sup- 
ported as in Fig. 28, upon an insulating stand, and to 
which silk strings were attached, by which it could be 
turned inside out. It was charged, and the charge was 
shown by the proof-plane and electroscope to be on the 
outside of the bag. On turning it inside out the elec- 




Fig. 28. 

tricity was once more found outside. Faraday's most 
striking experiment was made with a hollow cube, 
measuring 12 feet each way, built of wood, covered with 
tinfoil, insulated, and charged with a powerful machine, 
so that large sparks and brushes were darting off from 
every part of its outer surface. Into this cube Faraday 
took his most delicate electroscopes ; but once within he 
failed to detect the least effect upon them. 

35. Applications. — Advantage is taken of this in 
the construction of delicate electrometers and other 



42 ELECTRICITY AND MAGNETISM part i 

instruments, which can be effectually screened from 
the influence of electrified bodies by enclosing them 
in a cover of thin metal, closed all round, except where 
apertures must be made for purposes of observation. 
Metal gauze answers excellently, and is nearly trans- 
parent. It was proposed by the late Professor Clerk 
Maxwell to protect buildings from lightning by covering 
them on the exterior with a network of wires. 

36. Apparent Exceptions. — There are two apparent 
exceptions to the law that electrification resides only on 
the outside of conductors. (1) If there are electrified 
insulated bodies actually placed inside the hollow con- 
ductor, the presence of these electrified bodies acts 
inductively and attracts the opposite kind of charge to 
the inner side of the hollow conductor. (2) When elec- 
tricity flows in a current, it flows through the substance 
of the conductor. The law is limited therefore to 
electricity at rest, — that is, to statical charges. 

37. Faraday's *< Ice-pail" Experiment. — One experi- 
ment of Faraday deserves notice, as showing the part 
played by induction in these phenomena. He gradually 
lowered a charged metallic ball into a hollow conductor 
connected by a wire to a gold-leaf electroscope (Fig. 29), 
and watched the effect. A pewter ice-pail being con- 
venient for his purpose, this experiment is continually 
referred to by this name, though any other hollow con- 
ductor — a tin canister or a silver nmg, placed on a 
glass support — would of course answer equally well. 
The following effects are observed : — Suppose the ball 
to have a + charge : as it is lowered into the hollow con- 
ductor the gold leaves begin to diverge, for the presence 
of the charge acts inductively, and attracts a — charge 
into the interior and repels a + charge to the exterior. 
The gold leaves diverge more and more until the ball 
is right within the hollow conductor, after which no 
greater divergence is obtained. On letting the ball 
touch the inside the gold leaves still remain diverging as 



DISTRIBUTION OF CHARGE 



43 



before, and if now the ball is pulled out it is fouud to 
have lost all its electrification. The fact that the gold 
leaves diverge no wider after the ball touched than they 
did just before, proves 




Fig. 29. 



that when the charged 
ball is right inside the 
hollow conductor the 
induced charges are 
each of them precisely- 
equal in amount to its 
own charge, and the in- 
terior negative charge 
exactly neutralizes the 
charge on the ball at 
the moment when they 
touch, leaving the 
equal exterior charge 
unchanged. An electric 
cage, such as this ice- 
pail, when connected 
with an electroscope 
or electrometer, affords an excellent means of examining 
the charge on a body small enough to be hung inside 
it. For W'ithout using up any of the charge of the body 
(which we are obliged to do when applying the method 
of the proof-plane) we can examine the induced charge 
repelled to the outside of the cage, which is equal in 
amount and of the same sign. If two equal charges of 
opposite kinds are placed at the same time within the 
cage no effects are produced on the outside. 

38. Distribution of Charge. — A charge of electricity 
is not usually distributed uniformly over the surfaces 
of bodies. Experiment shows that there is more elec- 
tricity on the edges and corners of bodies than upon 
their flatter parts. This distribution can be deduced 
from the theory laid down in Lesson XXL, but mean- 
time we will give some of the chief cases as they can be 



44 ELECTRICITY AND MAGNETISM part i 

shown to exist. The term Electric Density is used to 
signify the amount of electricity at any point of a sur- 
face; the electric density at a point is the number of units 
of electricity per unit of area (i.e. per square inch, or per 
square centimetre), the distribution being supposed uni- 
form over this small surface. 

(a) Sphere. — The distribution of a charge over an 
insulated sphere of conducting material is uniform, pro- 
vided the sphere is also isolated, that is to say, is remote 
from the presence of all other conductors and all other 
electrified bodies. The density is uniform all over it. 
This is symbolized by the dotted line round the sphere 



d 6 





) ( Mllllll!iikiiiIi^""""" "^ii|illilipM / 

€ 

Fig. 30. 

in Fig. .30 a, which is at an equal distance from the 
.sphere all round, suggesting an equal thickness of charge 
at every point of the surface. It must be remembered 
that the charge is not really of any perceptible thickness 
at all ; it resides on or at the surface, but cannot be said 
to form a stratum upon it. 

(J)) Cylinder with rounded Ends. — Upon an elongated 
conductor, such as is frequently employed in electrical 
apparatus, the density is greatest at the ends where the 
curvature of the surface is the greatest. 

(c) Two Spheres in contact. — If two spheres in con- 
tact with each other are insulated and charged, it is found 
that the density is greatest at the parts farthest from the 



CHAP. I DISTRIBUTION OF CHARGE 45 

point of contact, and least in the crevice between them. 
If the spheres are of unequal sizes the density is greater 
on the smaller sphere, which has the surface more curved. 
On an egg-shaped or pear-shaped conductor the density 
is greatest at the small end. On a cone the density is 
greatest at the apex ; and if the cone terminate in a 
sharp point the density there is very much greater than 
at any other point. At a point, indeed, the density of 
the collected electricity may be so great as to electrify 
the neighbouring particles of air, which then are repelled 
(see Art. 47), thus producing a continual loss of charge. 
For this reason points and sharp edges are always avoided 
on electrical apparatus, except Avhere it is specially desired 
to set up a discharge. 

(r/) Flat Disk. — The density of a charge upon a flat 
disk is greater, as we should expect, at the edges than on 
the flat surfaces ; but over the flat surfaces the distribu- 
tion is fairly uniform. 

These various facts are ascertained by applying a 
small proof-plane successively at various points of the 
electrified bodies and examining the amount taken up by 
the proof-plane by means of an electroscope or electrome- 
ter. Coulomb, who investigated mathematically as well 
as experimentally many of the important cases of distri- 
bution, employed the torsion balance to verify his calcu- 
la4;ions. He investigated thus the case of the ellipsoid of 
revolution, and found the densities of the charges at the 
extremities of the axis to be proportional to the lengths 
of those axes. He also showed that the density of the 
charge at any other point of the surface of the ellipsoid 
was proportional to the length of the perpendicular drawn 
from the centre to the tangent at that point. Riess also 
investigated several interesting cases of distribution. He 
found the density at the middle of the edges of a cube to 
be nearly two and a half times as great as the density at 
the middle of a face ; while the density at a corner of the 
cube was more than four times as great. 



46 ELECTRICITY AND MAGNETISM part i 

39. Redistribution of Charge. — If any portion of the 
charge of an insulated conductor be removed, the re- 
mainder of the charge will immediately redistribute itself 
over the surface in the same manner as the original 
charge, provided it be also isolated, i.e. that no other con- 
ductors or charged bodies be near to perturb the distri- 
bution by complicated effects of influence. 

If a conductor be charged with any quantity of elec- 
tricity, and another conductor of the same size and shape 
(but uncharged) be brought into contact with it for an 
instant and then separated, it will be found that the 
charge has divided itself equally between them. In the 
same way a charge may be divided equally into three 
or more parts by being distributed simultaneously over 
three or more equal and sirdilar conductors brought into 
contact and symmetrically placed. 

If two equal metal balls, suspended by silk strings, 
charged with unequal quantities of electricity, are brought 
for an instant into contact and then separated, it will be 
found that the charge has redistributed itself fairly, half 
the sum of the two charges being now the charge of each. 
This may even be extended to the case of charges of 
opposite signs. Thus, suppose two similar conductors to 
be electrified, one with a positive charge of 5 units and 
the other with 3 nnits of negative charge, when these are 
made to touch and separated, each will have a positive 
charge of 1 unit ; for the algebraic sum of ^- 5 and — 3 is 
+ 2, which, shared between the two equal conductors, 
leaves + 1 for each. 

40. Capacity of Conductors. — If the conductors be 
unequal in size, or unlike in form, the shares taken by 
each in this redistribution will not be equal, but will be 
proportional to the electric capacities of the conductors. 
The definition of capacity in its relation to electric 
quantities is given in Lesson XXL, Art. 271. We may, 
however, make the remark, that two insulated conductors 
of the same form, but of different sizes, differ in their 



CHAP. I ELECTRIC MACHINES 47 

electrical capacity ; for the larger one must have a larger 
amount of electricity imparted to it in order to electrify 
its surface to the same degree. The term potential is 
employed in this connexion, in the following way: — A 
given quantity of electricity will electrify an isolated body 
up to a certain " potential " (or power of doing electric 
work) depending on its capacity. A large quantity of 
electricity imparted to a conductor of small capacity will 
electrify it up to a very high potential ; just as a large 
quantity of water poured into a vessel of narrow capacity 
will raise the surface of the water to a high level in the 
vessel. The exact definition of Potential, in terms of 
energy spent against the electrical forces, is given in the 
lesson on Electrostatics (Art. 263). 

It will be found convenient to refer to a positively 
electrified body as one electrified to a positive or high 
potential; while a negatively electrified body may be 
looked upon as one electrified to a low or negative poten- 
tial. And just as w^e take the level of the sea as a zero 
level, and measure the heights of mountains above it, 
and the depths of mines below it, using the sea level as a 
convenient point of reference for differences of level, so 
we take the potential of the earth's surface (for the sur- 
face of the earth is always electrified to a certain degree) 
as zero potential, and use it as a convenient point of 
reference from which to measure differences of electric 
potential. 

Lesson V. — Electric Machines 

41. ■ For the purpose of procuring larger supplies of 
electricity than can be obtained by the rubbing of a rod 
of glass or shellac, electric machines have been devised. 
All electric machines consist of two parts, one for pro- 
ducing, the other for collecting, the electric charges. Ex- 
perience has shown that the quantities of -f- and — elec- 



48 ELECTRICITY AND MAGNETISM part i 

trification developed by friction upon the two surfaces 
rubbed against one another depend on the amount of 
friction, upon the extent of the surfaces rubbed, and also 
upon the nature of the substances used. If the two sub- 
stances employed are near together on the list of electrics 
given in Art. 6, the electrical effect of rubbing them 
together will not be so great as if two substances widely 
separated in the series are chosen. To obtain the highest 
effect, the most positive and the most negative of the 
substances convenient for the construction of a machine 
should be taken, and the greatest available surface of 
them should be subjected to friction, the moving parts 
having a sufficient pressure against one another compati- 
ble with tlie required velocity. 

The earliest form of electric machine was devised by 
Otto von Guericke of Magdeburg, and consisted of a 
globe of sulphur fixed upon a spindle, and pressed with 
the dry surface of the hands while being made to rotate ; 
with this he discovered the existence of electric sparks 
and the repulsion of similarly electrified bodies. Sir 
Isaac Xewton replaced Von Guericke's globe of sulphur 
by a globe of glass. A little later the form of the 
machine was improved by various German electricians ; 
Von Bose added a collector or "prime conductor," in the 
shape of an iron tube, supported by a person standing on 
cakes of resin to insulate him, or suspended by silken 
strings ; Winckler of Leipzig substituted a leathern 
cushion for the hand as a rubber; and Gordon of Erfurt 
rendered the machine more easy of construction by using 
a glass cylinder instead of a glass globe. The electricity 
was led from the excited cylinder or globe to the prime 
conductor by a metallic chain which hung over against 
the globe. A pointed collector was not employed until 
after Franklin's famous researches on the action of points. 
About 1760 De la Fond, Planta, Ramsden, and Cuthbert- 
son, constructed machines having glass plates instead of 
cylinders. All frictional machines are, however, now 



FRICTIONAL MACHINES 



49 



obsolete, having in recent years been quite superseded by 
the modern Influence Machines. 

42. The Cylinder Electric Machine. — The Cylinder 
Electric Machine consists of a glass cylinder mounted 
on a horizontal axis capable of being turned by a handle. 
Against it is pressed from behind a cushion of leather 
stuffed with horsehair, the surface of which is covered 
with a powdered amalgam of zinc or tin. A flap of silk 
attached to the cushion passes over the cylinder, covering 
its upper half. In front of the cylinder stands the 
"prime conductor," which is made of metal, and usually 




Fig. 31. 

of the form of an elongated cylinder with hemispherical 
ends, mounted upon a glass stand. At the end of the 
prime conductor nearest the cylinder is fixed a rod bear- 
ing a row of fine metallic spikes, resembling in form a 
rake ; the other end usually carries a rod terminated in 
a brass ball or knob. The general aspect of the machine 
is shown in Fig. 31. When the handle is turned the 
friction between the glass and the amalgam-coated sur- 
face of the rubber produces a copious electrical action, 
electricity appearing as a + charge on the glass, leaving 
the rubber with a — charge. The prime conductor col- 

E 



50 



ELECTRICITY AND MAGNETISM part i 



lects this charge by the following process : — The + charge 
being carried round on the glass acts inductively on the 
long insulated conductor, repelling a + charge to the far 
end ; leaving the nearer end — ly charged. The effect of 
the row of points is to emit a — ly electrified wind (see 
Art. 47) towards the attracting + charge upon the glass, 
which is neutralized thereby ; the glass thus arriving 
at the rubber in a neutral condition ready to be again 
excited. This action of the points is sometimes described, 
though less correctly, by saying that the points collect the 
-f charge from the glass. If it is desired to collect also 
the — charge of the rubber, the cushion must be supported 
on an insulating stem and provided at the back with a 
metallic knob. It is, however, more usual to use only 
the + charge, and to connect the rubber by a chain to 
"earth," so allowing the — charge to be neutralized. 

43. The Plate Electric Machine. — The Plate Machine, 
as its name implies, is constructed with a circular plate 

of glass or of ebo- 
nite, and is usually 
provided with two 
pairs of rubbers 
formed of double 
cushions, pressing 
the plate between 
them, placed at its 
highest and lowest 
point, and provided 
with silk flaps, each 
extending over a 
quadrant of the 
circle. The prime 
conductor is either 
double or curved 
^°' "■ round to meet the 

plate at the two ends of its horizontal diameter, and is 
furnished with two sets of spikes, for the same purpose 




CHAP. I USE OF FEICTIONAL MACHINES 51 

as the row of points in the cylinder machine. A common 
form of plate machine is shown in Fig. 32. The action 
of the machine is, in all points of theoretical interest, the 
same as that of the cylinder machine. Its advantages 
are that a large glass plate is more easy to construct than 
a large glass cylinder of perfect form, and that the length 
along the surface of the glass between the collecting row 
of points and the edge of the rubber cushions is greater 
in the plate than in the cylinder for the same amount of 
surface exposed to friction; for, be it remarked, when the 
two charges thus separated have collected to a certain 
extent, a discharge will take place along this surface, the 
length of which limits therefore the po^ver of the machine. 
In a more modern form, due to Le Roy, and modified by 
Winter, there is but one rubber and flap, occupying a 
little over a quadrant of the plate, and one collector or 
double row of points, while the prime conductor consists 
of a ring-shaped body. 

44. Electric Amalgam. — Canton, finding glass to be 
highly electrified when dipped into dry mercury, sug- 
gested the employment of an amalgam of tin with mercury 
as a suitable substance wherewith to cover the surface of 
the rubbers. Still better is Kienmayer's amalgam, con- 
sisting of equal parts of tin and zinc, mixed while molten 
with twice their weight of mercury. Bisulphide of tin 
("mosaic gold ") may also be used. These amalgams are 
applied to the cushions with a little stiff grease. They 
serve the double purpose of conducting away the negative 
charge separated upon the rubber during the action of 
the machine, and of affording as a rubber a substance 
which is more powerfully negative (see list in Art. 6) than 
the leather or the silk of the cushion itself. Powdered 
graphite is also good. 

45. Precautions in using Frictional Machines. — Sev- 
eral precautions must be observed in the use of elec- 
trical machines. Damp and dust must be scrupulously 
avoided. The surface of glass is hygroscopic, hence, 



52 ELECTRICITY AND JNIAGNETISM paet i 

except in the driest climates, it is necessary to warm 
the glass surfaces and rubbers to dissipate the liliii of 
moisture which collects. Glass stems for insulation may 
be varnished with a thin coat of shellac varnish, or 
with paraffin (solid). A few drops of anhydrous paraffin 
(obtained by dropping a lump of sodium into a bottle of 
paraffin oil), applied with a bit of flannel to the pre- 
viously warmed surfaces, hinders the deposit of moist- 
ure. A frictional machine which has nob been used for 
some months will require a fresh coat of amalgam on its 
rubbers. These should be cleaned and warmed, a thin 
uniform layer of tallow or other stiff grease is spread 
upon them, and the amalgam, previously reduced to a fine 
powder, is sifted over the surface. In spite of all pre- 
cautions friction machines are uncertain in their be- 
haviour in damp weather. This is the main reason why 
they have been superseded by influence machines, which 
do not need to be warmed. 

All points should be avoided in apparatus for frictional 
electricity except where they are desired', like the "col- 
lecting " spikes on the prime conductor, to let off a charge 
of electricity. All the rods, etc., in frictional apparatus 
are therefore made with rounded knobs. 

46. Experiments with the Electric Machine. — With 
the electric machine many pleasing and instructive ex- 
periments are possible. The phenomena of attraction and 
repulsion can be shown upon a large scale. Fig. 33 repre- 
sents a device known as the electric chimes,* in which 
two small brass balls hung by silk strings are set in 
motion and strike against the bells between which they 
are hung. The two outer bells are hung by metallic 
wires or chains to the knob of the machine. The third 
bell is hung by a silk thread, but communicates with the 
ground by a brass chain. The balls are first attracted to 

* Invented in 1752 by Franklin, for the purpose of warning him of the 
presence of atmospheric electricity, drawn from the air above his house by 
a pointed iron rod. 



CHAP. I EXPERIMENTS WITH M^iCHINES 



53 



the electrified outer bells, then repelled, and, having dis- 
charged themselves against the uninsulated central bell, 
are again attracted, and so vibrate to and fro. 

By another arrangenaent small figures or dolls cut out 
of pith can be made to dance up and down between a 
metal plate hung horizontally 
from the knob of the machine, 
and another flat plate an inch ^^ 
or two lower and communi- 
cating with "earth." 

Another favourite way of 
exhibiting electric repulsion 
is by means of a doll with 
long hair placed on the ma- 
chine ; the individual hairs 
stand on end when the ma- 
chine is worked, being re- 
pelled from the head, and 
from one another. A paper 
tassel will behave similarly 
if hung to the prime con- 
ductor. The most striking way of showing this pheno- 
menon is to place a person upon a glass-legged stool, 
making him touch the knob of the machine ; when the 
machine is worked, his hair, if dry, will stand on end. 
Sparks will pass freely between a person thus electrified 
and one standing upon the ground. 

The sparks from the machine may be made to kindle 
spirits of wine or ether, placed in a metallic spoon, con- 
nected by a wire, with the nearest metallic conductor 
that runs into the ground. A gas jet may be lit by 
passing a spark to the burner from the finger of the 
person standing, as just described, upon an insulating 
stool. 

47. Effect of Points ; Electric Wind. — The effect of 
points in discharging electricity from the surface of a con- 
ductor may be readily proved by numerous experiments. 




54 



ELECTRICITY AND MAGNETISM part i 



If the machine be in good working order, and capable of 
giving, say, sparks 4 inches long when the knuckle is 
presented to the knob, it will be found that, on fastening 
a fine pointed needle to the conductor, it discharges the 
electricity so effectually at its point that only the shortest 
sparks can be drawn at the knob, while a fine jet or brush 
of pale bkie light will appear at the point. If a lighted 
taper be held in front of the point, the flame will be 
visibly blown aside (Fig. 34) by the streams of electrified 
air repelled from the point. These air-currents can be 




Fiff. 34. 



felt with the hand. They are due to a mutual repulsion 
between the electrified air particles near the point and 
the electricity collected on the point itself. That this 
mutual reaction exists is proved by the electric fly or 
electric reaction-mill of Hamilton (Fig. 35), which con- 
sists of a light cross of brass or straw, suspended on a 
pivot, and having the pointed ends bent round at right 
angles. When placed on the prime conductor of the 
machine, or joined to it by a chain, the force of repulsion 
between the electricity of the points and that on the air 



CHAP. I ELECTEIC WINDS FROM POINTS 



55 





immediately in front of them drives the mill romid in 
the direction opposite to that in which the points are 
bent. It will even rotate if immersed in turpentine or 
petroleum. If the points of the 
fly are covered with small round 
lumps of wax it will not rotate, 
as the presence of the wax pre- 
vents the formation of any 
wind or stream of electrified 
particles. 

The electric wind from a 
point will produce a charge 
upon the surface of any insulat- 
ing body, such as a plate of 
ebonite or glass, held a few 
inches away. The charge may 
be examined by dusting red 
lead or lycopodium powder 
upon the surface. If a slip of 
glass or mica be interposed between the point and the 
surface against which the wind is directed, an electric 
shadow will be formed on the surface at the part so 
screened. 

48. Armstrong's Hydro-Electrical Machine. — The 
friction of a jet of steam issuing fiom a boiler, through 
a wooden nozzle, generates electricity. In reality it is 
the particles of condensed water in the jet which are 
directly concerned. Sir W. Armstrong, who investigated 
this source of electricity, constructed a powerful appara- 
tus, known as the hydro-electrical machine, capable of 
producing enormous quantities of electricity, and yield- 
ing sparks 5 or 6 feet long. The collector consisted of 
a row of spikes, placed in the path of the steam jets 
issuing from wooden nozzles, and was supported, together 
with a brass ball which served as prime conductor, upon 
a glass pillar. 

49. Influence Machines. — There is another class of 



Fig. 35. 



56 ELECTRICITY AND MAGNETISM part i 

electrical machine, differing entirely from those we have 
been describing, and depending upon the principle of 
influence. They also have been termed convection-induc- 
tion machines^ because they depend upon the employment 
of a minute initial charge which, acting by influence, 
induces other charges, which are then conveyed by the 
moving parts of the machine to some other part, where 
they can be used either to increase the initial charge or to 
furnish a supply of electrification to a suitable collector. 
Of such instruments the oldest is the Electropliorus, ex- 
plained fully in Lesson IIL Bennet, Nicholson, Erasmus 
Darwin, and others devised pieces of apparatus for ac- 
complishing by mechanism that which the electrophorus 
accomplishes by hand. Nicholson's revolving doubter, in- 
vented in 1788, consists of a revolving apparatus, in which 
an insulated carrier can be brought into the presence of an 
electrified body, there touched for an instant while under 
influence, then carried forward with its acquired charge 
towards another body, to which it imparts its charge, and 
which in turn acts inductively on it, giving it an opposite 
charge, which it can convey to the first body, thus 
increasing its initial charge at every rotation. 

In the modern influence machines two principles are 
embodied : (1) the principle of influence, namely, that a 
conductor touched while under influence acquires a charge 
of the opposite kind ; (2) the principle of reciprocal accu- 
mulation. This principle must be carefully noted. Let 
there be two insulated conductors A and B electrified ever 
so little, one positively, the other negatively. Let a third 
insulated conductor C, which will be called a carrier, be 
arranged to move so that it first approaches A and then 
B, and so forth. If touched while under the influence 
of the small positive charge on A it will acquire a small 
negative charge ; suppose that it then moves on and 
gives this negative charge to B. Then let it be touched 
while under the influence of B, so acquiring a small 
positive charge. When it returns towards A let it give 



INFLUENCE MACHINES 



57 



up this positive charge to A, thereby increasing its 
positive charge. Then A will act more powerfully, and 
on repeating the former operations both B and A will 
become more highly charged. Each accumulates the 
charges derived by influence from the other. This is the 
fundamental action of the machines in question. The 
modern influence machines date from 1860, when C. F. 
Yarley produced a form vvitli six carriers mounted on a 
rotating disk of glass. This was followed in 1865 by 




the machine of Holtz and that of Toepler, and in 1867 
by those of Lord Kelvin (the " replenisher " and the 
"mouse-mill"). The latest forms are those of Mr. 
James AVimshurst. 

50. Typical Construction. — Before describing some 
special forms we will deal with a generalized type of 
machine having two fixed Jield-plates, A and B, which 
are to become respectively + and — , and a set of carriers, 
attached to a rotating disk or armature. Fig. 36 gives in 



58 ELECTRICITY AND MAGNETISM part i 

a diagrammatic way a view of the essential parts. For 
convenience of drawing it is shown as if the metal field- 
plates A and B were affixed to the outside of an outer 
stationary cylinder of glass ; the six carriers p, q, r, s, t, 
and u being attached to the inside of an inner rotating 
cylinder. The essential parts then are as follows : — 

(i.) A pair of Ji eld-plates A and B. 

(ii.) A set of rotating carriers p, q, r, s, t, and u. 

(iii.) A pair of neutralizing brushes ??j, Wg made of 
flexible metal wires, the function of which is 
to touch the carriers while they are under the 
influence of the field-plates. They are con- 
nected together by a diagonal conductor, which 
need not be insulated. 

(iv.) A pair of appropriating brushes a^, a^y^, which reach 
over from the field-plates to appropriate the 
charges that are conveyed around by the 
carriers, and impart them to the field-plates. 

(v.) In addition to the above, which are sufficient to 
constitute a complete self-exciting machine, it 
is usual to add a discharging apparatus, con- 
sisting of two combs Cj, Cg, to collect any unap- 
propriated charges from the carriers after they 
have passed the appropriating brushes ; these 
combs being connected to the adjustable dis- 
charging balls at D, 

The operation of the machine is as follows. The 
neutralizing brushes are set so as to touch the moving 
carriers just before they pass out of the influence of the 
field-plates. Suppose the field-plate A to be charged ever 
so little positively, then the carrier p, touched by n^ just 
as it passes, will acquire a slight negative charge, which 
it will convey forward to the appropriating brush a^ and 
will thus make B slightly negative. Each of the carriers 
as it passes to the right over the top will do the same 
thing. Similarly each of the carriers as it passes from 



CHAP. I INFLUENCE MACHINES 59 

right to left at the lower side will be touched by n^ while 
under the influence of the — charge on B, and will 
convey a small + charge to A through the appropriating 
brush «<,. In this way A will rapidly become more and 
more +, and B more and more — ; and the more highly 
charged they become, the more do the collecting combs 
Cj and Cg receive of unappropriated charges. Sparks will 
snap across between the discharging knobs at D. 

The machine will not be self-exciting unless there is a 
good metallic contact made by the neutralizing brushes and 
by the appropriating brushes. If the discharging apparatus 
were fitted at c^, c^ with contact brushes instead of spiked 
combs, the machine would be liable to lose the charge of 
the field-plates, or even to have their charges reversed in 
sign whenever a large spark was taken from the knobs. 

It will be noticed that there are two thicknesses of 
glass between the &xed Jleld-plates and the rotating carriers. 
The glass serves not only to hold the metal parts, but 
prevents the possibility of back-discharges (by sparks or 
winds) from the carriers to the field-plates as they pass. 

The essential features thus set forth will be found in 
Varley's machine of 1860, in Lord Kelvin's "replenisher" 
(which had only two carriers), and in many other machines 
including .the apparatus known as Clarke's "gas-lighter." 

51. Toepler's Influence Machine. — In this machine, 
as constructed by Voss, are embodied various points due 
to Holtz and others. Its construction follows almost 
literally the diagram already explahied, but instead of 
having two cylinders, one inside the other, it has two 
flat disks of varnished glass, one fixed, the other slightly 
smaller rotating in front of it (Fig. 37). The Jield-plates 
A and B consist of pieces of tinfoil, cemented on the 
back of the back disk, each protected by a coating of 
varnished paper. The carriers are small disks or sectors 
of tinfoil, to the number of six or eight, cemented to the 
front of the front disk. To prevent them from being- 
worn away by rubbing against the brushes a small 



60 



ELECTRICITY AND MAGNETISM part i 



metallic button is attached to the middle of each. The 
neutralizing brushes ??p ;?2 are small whisps of fine 
springy brass wire, and are mounted on the ends of a 
diagonal conductor Z. The appropriating brushes a^. a^ 
are also of thin brass wire, and are fastened to clamps 
projecting from the edge of the fixed disk, so that they 
communicate metallically with the two field-plates. The 
collecting combs, which have brass spikes so short as not 
to touch the carriers, are mounted on insulating pillars 
and are connected to the adjustable discharging knobs 




FRONT ROTATING DISK 
WITH CARRIERS ON FRONT. 



Fig. 37. 



Dj. Do- These also communicate with two small Leyden 
jars Jj, Jg, the function of which is to accumulate the 
charges before any discharge takes place. These jars are 
separately depicted in Fig. 38. Without them, the dis- 
charges between the knobs take place in frequent thin 
blue sparks. AVith them the sparks are less numerous, 
but very brilliant and noisy. 

To use the Toepler (Yoss) machine first see that all 
the four brushes are so set as to make good metallic con- 
tact with the carriers as they move past, and that the 



CHAP. I TOEPLER (VOSS) INFLUENCE MACHINE 61 

neutralizing brushes are set so as to touch the carriers 
while under influence, 'ilien see that the discharging 
knobs are drawn widely apart. Set the machine in 
rotation briskly. If it is clean it should excite itself 
after a couple of turns, and will emit a gentle hissing 
sound, due to internal discharges (visible as blue glimmers 
in the dark), and will offer more resistance to turning. 
If then the knobs are pushed nearer together sparks will 
pass across between them. The Jars (the addition of 
which we owe to Holtz) should be kept free from dust. 
Sometimes a pair of terminal screws are added at Sj, Sg 
(Fig. 38), connected respectively with the outer coatings 



Ji 




ifll!ii!illl!!!lim'!ll!llllliil!llil!lli!iiil!!J!i!:iil!i;!lillliil!li 
Fig. 33. 



of the jars. These are convenient for attaching wires to 
lead away discharges for experiments at a distance. If 
not so used they should be joined together by a short 
wire, as the two jars will not work properly unless their 
outer coatings are connected. 

52. Wimshurst's Influence Machine. — In this, the 
most widely used of influence machines, there are no 
fixed field-plates. In its simplest form it consists (Fig. 
39) of two circular plates of varnished glass, which are 
geared to rotate in opposite directions. A number of 
sectors of metal foil are cemented to the front of the 
front plate and to the back of the back plate ; these 
sectors serve both as carriers and as inductors. Across 



62 ELECTRICITY AND MAGNETISM part i 

the front is fixed an uninsulated diagonal conductor, 
carrying at its ends neutralizing brushes, which touch 
the front sectors as they pass. Across the back, but 
sloping the other way, is a second diagonal conductor, 
with brushes that touch the sectors on the hinder plate. 
Nothing more than this is needed for the machine to 
excite itself when set in rotation ; but for convenience 




Fig. 39. 
there is added a collecting and discharging apparatus. 
This consists of two pairs of insulated combs, each pair 
having its spikes turned inwards toward the revolving 
disks, but not touching them; one pair being on the 
right, the other on the left, mounted each on an insulat- 
ing pillar of ebonite. These collectors are furnished 
with a pair of adjustable discharging knobs overhead; 



CHAP. I WIMSHUEST INFLUENCE MACHINE 



63 



and sometimes a pair of Levden jars is added, to prevent 
the sparks from passing until considerable quantities of 
charge have been collected. 

The processes that occur in this machine are best 
explained by aid of a diagram (Fig. 40), in which, for 
greater clearness, the two rotating plates are represented 




FiiT. 40. 



as though they were two cylinders of glass, rotating 
opposite ways, one inside the other. The inner cylinder 
will represent the front plate, the outer the back plate. 
In Figs. 39 and 40 the front plate rotates right-handedly, 
the back plate left-handedly. The neutralizing brushes 
Wj, rio touch the front sectors, while n^, n^ touch against 
the back sectors. 



64 ELECTRICITY AND MAGNETISM part i 

Now suppose any one of the back sectors represented 
near the top of the diagram to receive a slight positive 
charge. As it is moved onward toward the left it will 
come opposite the place where one of the front sectors is 
moving past the brush riy ' The result will be that the 
sector so touched while under influence by n^ will acquire 
a slight negative charge, which it will carry onwards 
toward the right. When this negatively-charged front 
sector arrives at a point opposite n^ it acts inductively on 
the back sector which is being touched by n^; hence 
this back sector will in turn acquire a positive charge, 
which it will carry over to the left. In this way all the 
sectors will become more and more highly charged, the 
front sectors carrying over negative charges from left to 
right, and the back sectors carrying over positive charges 
from right to left. At the lower half of the diagram a 
similar but inverse set of operations will be taking place. 
For when n^ touches a front sector under the influence of 
a positive back sector, a repelled charge will travel along 
the diagonal conductor to n^, helping to charge positively 
the sector which it touches. The front sectors, as they 
pass from right to left (in the lower half), will carry 
positive charges, while the back sectors, after touching 
n^, will carry negative charges from left to right. The 
metal sectors then act both as carriers and as inductors. 
It is clear that there will be a continual carrying of posi- 
tive charges toward the right, and of negative charges 
to the left. At these points, toward which the opposite 
kinds of charges travel, are placed the collecting-combs 
communicating with the discharging knobs. The latter 
ought to be opened wide apart when starting the machine, 
and moved together after it has excited itself. 

In larger Wimshurst influence machines two, three, 
or more pairs of oppositely-rotating plates are mounted 
within a glass case to keep off the dust. If the neutral- 
izing brushes make good metallic contact these machines 
are all self -exciting in all weathers. Machines- with only 



CHAP. I 



HOLTZ INFLUENCE ^MACHINE 



65 



six or eight sectors on each plate give longer sparks, but 
less frequently than those that have a greater number. 
Mr. Winishurst has designed many influence machines, 
from small ones with disks 2 inches across up to that at 
South Kensington, which has plates 7 feet in diameter. 

Prior to Wimshurst's machine Holtz had constructed 
one with two oppositely-rotating glass disks; but they 
had no metal carriers upon them. It was not self -exciting. 

53. Holtz's Influence Machine. — The Holtz machine 
in its typical form had the following peculiarities. 
There were no metal carriers upon the rotating plate, 
hence another mode of charging it had to be adopted in 
lieu of touching conductors 
while under influence, 
as will be seen. The 
field-plates A and B (Fig. 
41) were of varnished 
paper — a poor conductor 
— fastened upon the back 
of the fixed disk. In the 
fixed disk of glass, on 
which the field-plates were 
mounted, there were cut 
two windows or openings, 
through which there pro- 
jected from the field-plates two pointed paper tongues, 
which took the place of appropriating brushes. The 
discharging knobs were inserted in the neutralizing cir- 
cuit which united two metal combs with pointed spikes, 
situated in front of the rotating front disk, opposite the 
two field-plates. There was (at first) no diagonal con- 
ductor. It will be noted that while the combs, which 
served both as neutralizing and collecting combs, were in 
front of the rotating plate, the appropriating tongues 
were situated at the back of the same. Fig. 41 is a 
view of the machine from behind. The machine was 
not self-exciting. In operating it the following procedure 




Fig. 41. 



66 ELECTRICITY AND MAGNETISM part i 

was used: first the two discharging knobs were put 
together, then the front disk was set into rapid rotation. 
AVhile so rotating a small initial charge was communi- 
cated to one of the field-plates by holding to it a rubbed 
piece of ebonite or glass, or by sending into it a spark 
from a Leyden jar. Thereupon the machine charged 
itself, and began to emit pale blue sparks from the points 
of the combs and tongues with a hissing sound. On then 
drawing apart the discharging knobs, a torrent of sparks 
rushed across. 

These arrangements being known, it is not difiicult 
to follow the action of the machine, provided it is once 
understood that the whole operation depends upon the 
circumstance that the surface of a non-conducting body 
such as glass can be electrified by letting off against it 
an electric wind from a point placed near it (see Art. 47). 
Suppose that a small initial -f charge is given to A. This 
will operate by influence upon the metal parts imme- 
diately opposite it, and cause the spikes to become elec- 
trified negatively, and to give off a negatively electrified 
wind, which will charge the face of the rotating plate, 
these charges being then carried over to the other side, 
where the spikes of the other comb will be emitting a 
positively electrified wind. The pointed tongues which 
project towards the back of the rotating disk also let off 
winds, the tendency being always for them to charge the 
back of the plate with a charge of opposite sign from 
that which is coming toward them on the front. If 
negative charges are being carried over the top on the 
front, then the tongue of B will tend to let off a positive 
charge against the back, thereby leaving B more negative. 
In the same way the tongue of A will let off a negatively 
electrified wind, making A more positive, so building up 
or accumulating two opposite kinds of charges on the 
two field-plates. This action will not occur unless the 
moving plate rotates in the direction opposite to that in 
which the two tongues point. 



CHAP. I HOLTZ INFLUENCE MACHINE 67 

The defects of the Holtz machine were that it was so 
sensitive to damp weather as to be unreliable, that it was 
apt suddenly to reverse its charges, and that the electric 
winds by which it operated could not be produced with- 
out a sufficiently great initial charge. 

In later Holtz machines a number of rotating disks 
fixed upon one common axis were employed, the whole 
being enclosed in a glass case to prevent the access of 
damp. A small disk of ebonite was sometimes fixed to 
the same axis, and provided with a rubber, in order to 
keep up the initial charge by friction. Holtz constructed 
many forms of machine, including one with thirty-two 
plates, besides machines of a second kind having two 
glass plates rotating in opposite directions. 

The Holtz machine, as indeed every kind of influence 
machine, is reversible in its action ; that is to say, that if 
a continuous supply of the two electricities (furnished by 
another machine) be communicated to the armatures, the 
movable plate will be thereby set in rotation and, if 
allowed to run quite freely, will turn in an opposite sense. 

Kighi showed that a Holtz machine can yield a con- 
tinuous current like a voltaic battery, the strength of 
the current being nearly proportional to the velocity of 
rotation. It was found that the electromotive-force of a 
machine was equal to that of 52,000 Daniell's cells, or 
nearly 53,000 volts, at all speeds. The resistance when 
the machine made 120 revolutions per minute was 2810 
million ohms ; but only 646 million ohms when making 
450 revolutions per minute. 

54. Experiments with Influence Machines. — The 
experiments described in Art. 43, and indeed all those 
usually made with the old frictional machines, includ- 
ing the charging of Ley den jars, can be performed 
by the aid of influence machines. In some cases it is 
well to connect one of the two discharging knobs to the 
earth by a wire or chain, and to take the discharge from 
the other knob. To illuminate small vacuum tubes they 



68 ELECTEICITY AXD MAGXETISM part i 

may be connected by guttapercha-covered wii'es to the 
two discharging knobs, or to the terminals S^ So of 
Fig. 38. The curious pro^jerty of the electric discharge 
from a point in collecting dust or fumes is readily shown 
by connecting by a wire a needle which is introduced 
into a bell-jar of glass. The latter is filled with fumes 
by burning inside it a bit of magnesium wii'e, or of brown 
paper. Then on turning the handle of the influence 
machine the fumes are at once deposited, and the air left 
clear. 



Lesson YI. — The Leyden Jar and other Condensers 

5d. It was shown in previous lessons that the opposite 
charges of electricity attract one another ; that electricity 
cannot flow tkrough glass ; and that yet electricity can 
act across glass by influence. Two suspended pith-balls, one 
electrified positively and the other negatively, will attract 
one another across the intervening air. If a plate of glass 
be put between them they will still attract one another, 
though neither they themselves nor the electric charges 
on them can j)ass through the glass. If a pith-ball 
electrified with a — charge be hung inside a dry glass 
bottle, and a rubbed glass rod be held outside, the pith- 
ball will rush to the side of the bottle nearest to the glass 
rod, being attracted by the 4- charge thus brought near it. 
If a pane of glass be taken, and a piece of tinfoil be stuck 
upon the middle of each face of the pane, and one piece 
of tinfoil be charged positively, and the other negatively, 
the two charges will attract oue another across the glass, 
and vrnl no longer be found to be free. If the pane is 
set up on edge, so that neither piece of tinfoil touches the 
table, it will be found that hardly any electricity can be 
got by merely touching either of the foils, for the charges 
are "bound," so to speak, by each other's attra-ctions ; 
each charge is inducing the other. In fact it will be 



CHAP, I 



CONDENSERS 



69 



found that these two pieces of tinfoil may be, in this 
manner, charged a great deal more strongly than either of 
them could possibly be if it were stuck to a piece of glass 
alone, and then electrified. In other words, the capacity 
of a conductor is greatly increased ivlien it is placed near to a 
conductor electrijied with the opposite kind of charge. If its 
capacity is increased, a greater quantity of electricity may 
be put into it before it is charged to an equal degree of 
potential. Hence, such an arrangement for holding a 
large quantity of electrification may be called a condenser 
of electricity. 

56. Condensers. — Next, suppose that we have two 
brass disks, A and B (Fig. 42), set upon insulating stems, 
and that a glass plate is placed between them. Let B be 
connected by a wire 
to the knob of an 
electrical machine, 
and let A be joined 
by a wire to "earth." 
The + charge upon 
B will act induc- 
tively across the 
glass plate on A, 
and will repel elec- Fig. 42. 

tricity into the earth, 

leaving the nearest face of A negatively electrified. This 
— charge on A will attract the + charge of B to the side 
nearest the glass, and a fresh supply of electricity will come 
from the machine. Thus this arrangement will become a 
condenser. If the two brass disks are pushed up close to 
the glass plate there will be a still stronger attraction 
between the + and — charges, because they are now nearer 
one another, and the inductive action will be greater; hence 
a still larger quantity can be accumulated in the plates. 
We see then that the capacity of a condenser is increased 
by bringing the plates near together. If now, while the 
disks are strongly charged, the wires are removed and the 





70 ELECTRICITY AND MAGNETISM part i 

disks are drawn backwards from one another, the two 
charges will not hold one another bound so strongly, and 
there will be more free electrification than before over their 
surfaces. This would be rendered evident to the experi- 
menter by the little pith-ball electroscopes fixed to them 
(see the Fig.), which would fly out as the brass disks were 
moved apart. We have put no further charge on the 
disk B, and yet, from the indications of the electroscope, 
we should conclude that by moving it away from disk A 
it has become electrified to a higher degree. The fact is, 
that while the conductor B was near the — charge of A 
the capacity of B was greatly increased, but on moving it 
away from A its capacity has diminished, and hence the 
same quantity of electricity now electrifies it to a higher 
degree than before. The presence, therefore, of an earth- 
connected plate near an insulated conductor increases its 
capacity, and permits it to accumulate a greater charge 
by attracting and condensing the electricity upon the face 
nearest the earth-plate, the surface-density on this face 
being therefore very great ; hence the appropriateness of 
the term condenser as applied to the arrangement. It was 
formerly also called an accumulator ; but the term accu- 
mulator is now reserved for the special kind of battery for 
storing the energy of electric currents (Art. 492). 

The stratum of air between the two disks will sufiice 
to insulate the two charges one from the other. The 
brass disks thus separated by a stratum of air constitute 
an air-condenser, or air-leyden. Such condensers were 
first devised by Wilcke and Aepinus. In these experi- 
ments the sheet of glass or layer of air acts as a dielectric 
(Art. 295) conveying the inductive action through its 
substance. All dielectrics are insulators, but equally 
good insulators are not necessarily equally good dielec- 
trics. Air and glass are far bettei- insulators than ebonite 
or paraffin in the sense of being much worse conductors. 
But influence acts more strongly across a slab of glass 
than across a slab of ebonite or paraffin of equal thickness. 



HAP. I DISPLACEMENT 71 

.nd better still across these than across a layer of air. In 
tther ^yords, glass is a better dielectric than ebonite, or 
)araffin, or air, as it possesses a higher inductive capacity. 

It ^Yill then be seen that in the act of charging a con- 
Lenser, as much electricity flows out at one side as flows 
n at the other. 

67. Displacement. — AVhenever electric forces act on 
, dielectric, tending to drive electricity in at one side and 
>ut at the other, we may draw lines of force through the 
lielectric in the direction of the action, and we may con- 
ider tubular spaces mapped out by such lines. We may 
onsider a tube of electric force having at one end a 
lefinite area of the positively charged surface, and at the 
)ther end an area of the negatively charged surface, 
rhese ^reas may be of different size or shape, but the 
quantities of + and — electrification over them wdll be 
iqual. The quantity of electricity which has apparently 
)een transferred along the tube was called by Maxwell 
'the displacement.'" In non-conductors it is proportional 
o the electromotive-force. In conductors electromotive 
orces produce currents, which may be regarded as dis- 
)lacements which increase continuously with time. In 
:ertain crystalline media the displacement does not take 
)lace exactly in the direction of the electric force : in 
his case we should speak of tubes of influence rather 
han tubes of force. A unit tube will be bounded at its 
wo ends by unit charges -}- and —. We may consider 
he whole electric field between positively and negatively 
;harged bodies as mapped out into such tubes. 

58. Capacity of a Condenser. — It appears, therefore, 
hat the capacity of a condenser will depend upon — 

(1) The size and form of the metal plates or coatings. 

(2) The thinness of the stratum of dielectric between 

them ; and 

(3) The dielectric capacity of the material. 

59. The Leyden Jar. — The Leyden jar, called after 
he city where it was invented, is a convenient form of 



72 



ELECTRICITY A^'D MAGNETISM part 




condenser. It usually consists (Fig. 43) of a glass jar 
coated up to a certain height on the inside and outside 
with tinfoil. A brass kuob fixed on the end of a stout 
brass wire passes downward through a lid or top of dry 
well-varnished wood, and communicates by a loose bit of 
brass chain with the inner coating of foil. To charge the 
jar the knob is held to the prime conductor of an electrical 
machine, the outer coating- 
being either held in the hand 
or connected to " earth " by a 
wire or chain. TThen a + 
charge of electricity is im- 
parted thus to the inner coat- 
ing, it acts inductively on the 
outer coating, attractijig a — 
charge into the face of the 
outer coating nearest the glass, 
"pTJ""^ and repelling a + charge to the 

outside of the outer coating, 
and thence through the hand or wire to earth. After 
a few moments the jar will have acquired its full 
charge, the outer coating being- and the inner +. If 
the jar is of good glass, and dry, and free from dust, it 
will retain its charge for many hours or days. But if a 
path be provided by which the two mutually attracting 
electricities can flow to one another, they will do so, and 
the jar will be instantaneously discharged. If the outer 
coating be grasped with one hand, and the knuckle of the 
other hand be presented to the knob of the jar, a bright 
spark will pass between the knob and the knuckle with 
a sharp report, and at the same moment a convulsive 
*' shock " will be communicated to the muscles of the 
wrists, elbows, and shoulders. A safer means of dis- 
charging the jar is afforded by the discharging tongs 
or discharger (Fig. 44), which consists of a jointed brass 
rod provided with brass knobs and a glass handle. One 
knob is laid against the outer coating, the other is then 



LEYDEN JAR 73 




brought near the knob of the jar, and a bright snapping 

spark leaping from knob to knob announces that the two 

accuniLilated charges have flowed 

together, completing the discharge. 

Sometimes a jar discharges itself by 

a spark climbing over the top edge of 

the jar. Often when a jar is well 

charged a hissing sound is heard, due 

to partial discharges creeping over 

the edge. They can be seen in the 

dark as pale phosphorescent streams. 

60. Discovery of the Ley den Jar. 
— The discovery of the Le3^den jar 
arose from the attempt of Musschen- 
broek and his pupil Cuneus * to col- ^' 

lect the supposed electric " fluid " in a bottle half filled 
with water, which was held in the hand and was provided 
with a nail to lead the " fluid " down through the cork 
to the water from the electric machine. Here the water 
served as an inner coating and the hand as an outer 
coating to the jar. Cuneus on touching the nail received 
a shock. This accidental discovery created the greatest 
excitement in Europe and America. 

61. Residual Charges. — If a Leyden jar be charged 
and discharged and then left for a little time to itself, 
it w^ill be found on again discharging that a small 
second spark can be obtained. There is in fact a 
residual charge which seems to have soaked into the 
glass or been absorbed. The return of the residual 
charge is hastened by tapping the jar. The amount of 
the residual charge varies with the time that the jar has 
been left charged; it also depends on the kind of the 
glass of which the jar is made. There is no residual 
charge discoverable in an air-leyden after it has once 
been discharged. 

* The honour of the invention of the jar is also claimed for Kleist, 
Bishop of Pomerania. 



74 



ELECTRICITY AND MAGNETISM part i 



62. Batteries of Leyden Jars. — A large Leyden jar 
will give a more powerful shock than a small one, for a 
larger charge can be put into it ; its capacity is greater. 
A Leyden jar made of thin glass has a greater capacity 
as a condenser than a thick one of the same size ; but if 
it is too thin it will be destroyed when powerfully charged 




Fig. 45. 

by a spark actually piercing the glass. " Toughened " 
glass is less easily pierced than ordinary glass, and hence 
Leyden jars made of it may be made thinner, and so will 
hold a greater charge. To prevent jars from being pierced 
by a spark, the highest part of the inside coating should 
be connected across by a strip of foil or a metallic disk 
to the central wire. 

If a jar is desired to give long sparks, there must be 



LEYDEN JARS 



75 



left a long space of varnished glass above the top of the 
coatings. 

If it is desired to accumulate a very great charge of 
electricity, a number of jars must be employed, all their 
inner coatings being connected together, and all their 
outer coatings being united. This arrangement is called 
a battery of Leyden jars, or Leyden battery (Fig. 45). 
As it has a large capacity, it -uill require a large quantity 
of electricity to charge it fully. When charged it pro- 
duces very powerful effects ; its spark will pierce glass 
readily, and every care must be 
taken to avoid a shock from it 
passing through the person, as it 
might be fatal. The "Universal 
Discharger " as employed with the 
Leyden battery is shown at the 
right of the figure. 

63. Seat of the Charge. — Ben- 
jamin Franklin discovered that the 
charges of the Leyden jar really 
reside on the surface of the glass, 
not on the metallic coatings. This 
he proved by means of a jar whose 
coatings could be removed (Fig. 
46). The jar was charged and 
placed upon an insulating stand. 
The inner coating was then lifted 
out, and the glass jar was then 
taken out of the outer coating. 
Il^either coating was found to be 
electrified to any extent, but on 
again putting the jar together it 
was found to be highly charged. The charges had all the 
time remained upon the inner and outer surfaces of the 
glass dielectric. 

64. Dielectric Strain. — Farady proved that the me- 
dium across which influence takes place really plays an 




Fig. 46. 



76 ELECTRICITY AXD MAG^'ETISM pari i 

important part in the phenomena. It is now known 
that all dielectrics across which inductive actions are at 
work are thereby strained.'^ Inasmach as a good vacuum 
is a good dielectric, it is clear that it is not necessarily 
the material particles of the dielectric substance that are 
thus aifected; hence it is believed that electrical pheno- 
mena are due to stresses and strains in the so-called 
•• ether," the thin naediura pervading all matter and all 
space, whose highly elastic constitution enables it to con- 
vey to us the vibrations of light though it is millions of 
times less dense than air. As the particles of bodies are 
intim.ately surrounded by ether, the strains of the ether 
are also communicated to the particles of bodies, and they 
too suifer a strain. The glass between the tw'o coatings 
of tinfoil in the Ley den jar is actually strained or 
squeezed, there being a tension along the lines of electric 
force. When an insulated charged ball is hung up in a 
room an equal amount of the opposite kind of charge is 
attracted to the inside of the walls, and the air between 
the ball and the walls is strained (electrically) like the 
glass of the Leyden jar. If a Leyden jar is made of thin 
glass it may give way under the stress; and when a 
Leyden jar is discharged the layer of air between the 
knob of the jar and the knob of the discharging tongs is 
more and more strained as they are approached towards 
one another, tiU at last the stress becomes too great, and 
the layer of air gives way, and is -perforated" by the 
spark that discharges itself across. The existence of such 
stresses enables us to understand the residual charge of 
Leyden jars in which the glass does not recover itself all 
at once, by reason of its viscosity, fi'om the strain to 
which it has been subjected. It must never be for- 
gotten that electric force acts across space in conse- 
quence of the transmission of stresses and strains in the 

* In the exact sciences a strain means an alteration of form or volume 
due to the application of a stress. A stress is the forc«, pressure, or other 
agency which produces a strain. 



CHAP. I OTHER SOURCES 77 

medium with which space is filled. In every case we 
store not electricity but energy. Work is done in push- 
ing electricity from one place to another against the 
forces which tend to oppose the movement. The charg- 
ing of a Leyden jar may be likened to the operation of 
bending a spring, or to pumping up water from a low 
level to a high one. In charging a jar we pump exactly 
as much electricity out of the negative side as we pump 
into the positive side, and we spend energy in so doing. 
It is this stored energy which afterwards reappears in 
the discharge. 



Lesson VII. — Other Sources of Electrification 

Q5. It was remarked at the close of Lesson I. 
(p. 13) that friction was by no means the only source 
of electricity. Some of the other sources will now be 
named. 

GQ. Percussion. — A violent blow struck by one sub- 
stance upon another produces opposite electrical states 
on the two surfaces. It is possible indeed to draw up a 
list resembling that of Art. 6, in such an order that each 
substance will take a + charge on being struck with one 
lower on the list. 

67. Vibration. — Volpicelli showed that vibrations 
set up within a rod of metal coated with sulphur or 
other insulating substance, produced a separation of 
electricities at the sm^face separating the metal from the 
non-conductor. 

68. Disruption and Cleavage. — If a card be torn 
asunder in the dark, sparks are seen, and the separated 
portions, when tested with an electroscope, will be found 
to be electrical. The linen faced with paper used in 
making strong envelopes and for paper collars, shows 
this very well. Lumps of sugar, crunched in the dark 
between the teeth, exhibit pale flashes of light. The 



78 ELECTRICITY AND MAGNETISM part i 

sudden cleavage of a sheet of mica also produces sparks, 
and both laminse are found to be electrified. 

69. Crystallization and Solidification. — Many sub- 
stances, after passing from the liquid to the solid state, 
exhibit electrical conditions. Sulphur fused in a glass 
dish and allowed to cool is violently electrified, as may- 
be seen by lifting out the crystalline mass with a glass 
rod. Chocolate also becomes electrical during solidifica- 
tion. When arsenic acid crystallizes out from its solu- 
tion in hydrochloric acid, the formation of each crystal 
is accompanied by a flash of light, doubtless due to an 
electrical discharge. A curious case occurs w^hen the 
sulphate of copper and potassium is fused in a crucible. 
It solidifies without becoming electrical, but on cooling 
a little further the crystalline mass begins to fly to 
powder wdth an instant evolution of electricity. 

70. Combustion. — Yolta showed that combustion 
generated electricity. A piece of burning charcoal, or a 
burning pastille, such as is used for fumigation, placed 
in connexion with the knob of a gold-leaf electroscope, 
will cause the leaves to diverge. 

71. Evaporation. — The evaporation of liquids is 
often accompanied by electrification, the liquid and 
the vapour assuming opposite states, though apparently 
only when the surface is in agitation. A few drops 
of a solution of sulphate of copper thrown into a hot 
platinum crucible produce violent electrification as they 
evaporate. 

72. Atmospheric Electricity. — The atmosphere is 
found to be always electrified relatively to the earth: 
this is due, in part possibly, to evaporation going on 
over the oceans. The subject of atmospheric electricity 
is treated of separately in Lesson XXY. 

73. Pressure. — A large number of substances when 
compressed exhibit electrification on their surface. Thus 
cork becomes -f when pressed against amber, gutta- 
percha, and metals: while it takes a - charge when 



CHAP. I PYRO-ELECTRICITY 79 

pressed against spars and animal substances. Peclet 
found the degree of electrification produced by rubbing- 
two substances togetlier to be independent of the pressure 
and of the size of tlie surfaces of contact, but depended 
upon the materials and on the velocity with which they 
moved over one another. Rolling contact and sliding 
friction produced equal effects. 

74. Pyro-electricity. — There are certain crystals 
which, while being heated or cooled, exhibit electrical 
charges at certain regions or poles. Crystals thus elec- 
trified by heating or cooling are said to be pyro-electric. 
Chief of these is the Tourmaline, whose power of attract- 
ing light bodies to its ends after being heated has been 
known for some centuries. It is alluded to by Theo- 
phrastus and Pliny under the name of Lapis Lyncurius. 
Tourmaline is a hard mineral, semi-transparent when 
cut into thin slices, and of a dark green or brown colour, 
but looking perfectly black and opaque in its natural 
condition, and possessing the power of polarizing light. 
It is usually found in slightly irregular three-sided 
prisms which, when perfect, are pointed at both ends. 
It belongs to the "hexagonal" system of crystals, but 
is only hemihedral, that is to say, has the alternate 
faces only developed. Its form is given in Fig. 47, where 
a general view is first shown, the two ends A and B 
being depicted in separate plans. These two ends differ 
slightly in shape. Each is made up of three sloping faces 
terminating in a point. But at A the edges between 
these faces run down to the corners of the prism, while 
in B the edges between the terminal faces run down to 
the middle points of the long faces of the prism. The 
end A is known as the analogous pole, and B as the 
antilogous pole. While the crystal is rising in tempera- 
ture A exhibits + electrification, B — ; but if, after hav- 
ing been heated, it is allowed to. cool, the polarity is 
reversed ; for during the time that the temperature 
is falling B is -f- and A is — . If the temperature is 



80 



ELECTRICITY AND MAGNETISM part i 



steady no such electrical effects are observed either at 
high or low temperatures ; and the phenomena cease if 
the crystal be warmed above 150° C. This is not, how- 
ever, due to the crystal becoming a conductor at that 
temperature; for its resistance at even higher tempera- 
tures is still so great as to make it practically a non- 
conductor. A heated crystal of tourmaline suspended 
by a silk fibre may be attracted and repelled by electri- 
fied bodies, or by a second heated tourmaline ; the two 
similar poles repelling one another, while the two poles 





w 



^.-^-"'C^/a'ip^^ 




V S^ 


r 


iloo 


01° 


a; 


_.// 


W" 


/ 



Fig. 47. 



Fig. 48. 



of opposite form attract one another. If a crystal be 
broken up, each fragment is found to possess also an 
analogous and an antilogous pole. 

Many other crystals beside the tourmaline are more 
or less pyro-electric. Amongst these are silicate of zinc 
("electric calamine"), boracite, cane-sugar, quartz, tar- 
trate of potash, sulphate of quinine, and several others. 
Boracite crystallizes in the form shown in Fig. 48, which 
represents a cube having four alternate corners truncated. 
The corners not truncated behave as analogous poles, the 
truncated ones as antilogous. When a natural hexagonal 
prism of quartz is heated its six edges are found to be -f 
and — in alternate order. 



CHAP. I 



PIEZO-ELECTKICITY 



81 



75. Piezo-electricity. — In certain crystals pressure 
in a particular direction may produce electrification. 
Haiiy found that a crystal of calcspar pressed between the 
dry fingers, so as to compress it along the blunt edges of 
the crystal, became electrical, and that it retained its 
electricity for some days. He even proposed to employ a 
squeezed suspended crystal as an electroscope. A similar 
property is alleged of mica, 

topaz, and fluorspar. If two 
opposite edges of a hexagonal 
prism of quartz are pressed 
together, one becomes +, the 
other — . Pressure also pro- 
duces opposite kinds of electri- 
fication at opposite ends of a 
crystal of tourmaline, and of 
other crystals of the class 
abeady noticed as possessing 
the peculiarity of skew-sym- 
metry or hemihedry in their 
structure. Piezo-electricity is 
the name given to this branch 
of the science. It is known 
that skew-symmetry of struc- 
ture is dependent on molecular 
constitution ; and it is doubt- 
less the same peculiarity which 
determines the pyro-electric 
and piezo-electric properties, 
as well as the optical behaviour 
of these crystals in polarized 
light. 

76. Animal Electricity. — 
Several species of creatures 

inhabiting the water have the power of producing 
electric discharges physiologically. The best known of 
these creatures are the Torpedo, the Gymnotus, and the 




Fi"-. 49. 



82 ELECTRICITY AND MAGNETISM part i 

Silurus. The Raia Torpedo,* or electric ray, of which 
there are three species inhabiting the Mediterranean and 
Atlantic, is provided with an electric organ on the back 
of its head, as shown in Fig. 49. This organ consists of 
laminag composed of polygonal cells to the number of 800 
or 1000, or more, supplied with four large bundles of 
nerve fibres ; the under surface of the fish is — , the upper 
+ . In the Gymnotus electricus, or Surinam eel (Fig. 50), 
the electric organ goes the whole length of the body from 
tail to head. Humboldt gives a lively account of the 




Fig. 50. 

combats between the electric eels and the wild horses, 
driven by the natives into the swamps inhabited by the 
Gynmotus. It is able to give a most terrible shock, and 
is a formidable antagonist when it has attained its full 
length of 5 or 6 feet. In the Silurus the current flows 
from head to tail. 

Nobili, Matteucci, and others, have shown that nerve- 
excitations and muscular contractions of human beings 
also give rise to feeble discharges of electricity. 

77. Electricity of Vegetables. — Buff thought he 
detected electrification produced by plant life ; the roots 
and juicy parts being negatively, and the leaves posi- 
tively, electrified. The subject has, however, been little 
investigated. 

* It is a curious point that the Arahian name for the torpedo, ra ad, 
signifies lightning. This is perhaps not so curious as that the Electra of 
the Homeric legends should possess certain qualities that would tend to 
suggest that she is a personification of the lightning. The resemblance 
between the names electra and electron (amber) cannot be accidental. 



CHAP. I ELECTRIFICATION BY CONTACT 



83 



78. Thermo-electricity. — Heat applied at the junc- 
tion of two dissimilar metals produces a flow of elec- 
tricity across the junction. This subject is discussed in 
Lesson XXXY. on Thermo-electric Currents. 

79. Contact of Dissimilar Metals. — Volta showed 
that the contact of two dissimilar metals in air produced 
opposite kmds of 

electrification, one 
becoming positively, 
and the other neg- 
atively, electrified. 
This he proved in 
several ways, one of 
the most conclusive 
proofs being that 
afforded by his con- 
densing electroscope. 
This consisted of a 
gold-leaf electroscope 
combined with a 
small condenser. A 
metallic plate formed 
the top of the electro- 
scope, and on this 
was placed a second 
metallic plate fur- 
nished with a handle, and insulated from the lower one 
by being well varnished at the surface (Fig. 51). As the 
capacity of such a condenser is considerable, a very feeble 
source may supply a quantity of electricity to the con- 
denser without materially raising its potential, or causing 
the gold leaves to diverge. But if the upper plate be lifted, 
the capacity of the lower plate diminishes enormously, 
and the potential of its charge rises as shown by the 
divergence of the gold leaves.* To prove by the con- 

* Formerly, this action was accounted for by saying that the electricity 
which was " bound " when the plates of the condenser were close together, 




Fig. 51. 



84 ELECTEICITY AXD MAGXETISM part i 

densing electroscope that contact of dissimilar metals does 
produce electi-ification. a small compound bar made of 
TWO dissimilar metals — say zinc and copper — soldered 
together, is held in the moist hand, and one end of it is 
touched against the lower plate, the upper plate being 
placed in contact with the gi'ound or touched with the 
finger. When the two opposing charges hare thtLS col- 
lected in the condenser the upper plate is removed, and 
the diverging of the gold leaves shows the presence of 
a free charge, which can afterwards be examined to see 
whether it be -f or — . Instead of employing the copper- 
zinc bar, a single voltaic cell may be connected by copper 
vrires to the two plates. For a long time the existence of 
this electrification by contact was denied, or rather it was 
declared to be due (when occurriug in voltaic combina- 
tions such as are described in Lesson 
XIII.) to chemical actions going on; 
whereas the real truth is that the 
electricity of contact and the chemical 
action are both due to molecular con- 
ditions of the stibstances which come 
into contact with one another, though 
we do not yet know the precise natm'e 
of the molecular conditions which give 
rise to these two effects. Later experiments, especially 
those made ^ith the modern delicate electrometers 
of Lord Kelvin, put beyond doubt the reality of 
Yolta's discovery. One simple experiment explains 
the method adopted. A thin strip or needle of metal 
is suspended so as to turn about a point C. It is 
electrified from a known source. Lender it are placed 
(Fig. 52) two semicircular disks, or half-rings of dissimilar 



becomes " free " -when the top plate is lifted up ; the above is. lioxreTer, a 
more scientific and more accm^te -war of saying the same thing. The 
student who is unable to reconcile these two ■ways of stating the matter 
should read again Articles -t) and 55, on pp. 46 and 65. A much more sensi- 
tive apparatus to show the effect is the quadrant electrometer (Art. 2^). 




CHAP. I CONTACT SERIES OF METALS 



86 



metals. i!^either attracts or repels the electrified needle 
until the two are brought into contact, or connected by a 
third piece of metal, when the needle immediately turns, 
being attracted by the one that is oppositely electrified, and 
repelled by the one that is electrified similarly with itself. 
80. Contact Series of Metals (in Air). — Volta 
found, moreover, that the differences of electric potential 
between the different pairs of metals were not all equal. 
Thus, while zinc and lead were respectively + and — to 
a slight degree, he found zinc and silver to be respec- 
tively + and — to a much greater degree. He was able 
to arrange the metals in a series such that each one 
enumerated became positively electrified when placed in 
contact in air with one below it in the series. Those 
in italics are added from observations made since Yolta's 
time — 

+ Sodium, Copper, 

Magnesium, Silver, 

Zinc, Gold, 

Lead, Platinum, 

Tin, — Graphite (Carbon). 

Iron, 

Though Yolta gave rough approximations, the actual 
numerical values of the differences of potential in air for 
different pairs of metals have only lately been measured 
by Ayrton and Perry, a few of whose results are tabu- 
lated here — 



Zinc 

Lead 

Tm 

Iron 

Copper 

Platinum 

Carbon 



Diflference of Potential 
(volts). 

•210 



•069 
•313 
•146 
•238 
•113 



86 ELECTRICITY AND MAGNETISM pakt i 

The difference of potential between zinc and carbon 
is the same as that obtained by adding the successive 
differences, or 1-09 volts.* Yolta's observations may 
therefore be stated in the following generalized form, 
known as Volta's Law. The difference of potential be- 
tween any two metals is equal to the sum of the differences 
of potentials between the intervening metals in the contact- 
series. 

It is most important to notice that the order of the 
metals in the contact-series in air is almost identical 
with that of the metals arranged according to their 
electro-chemical power, as calculated from their chemical 
equivalents and their heat of combination with oxygen 
(see Table, Art. 489). From this it would appear that 
the difference of potentials between a metal and the air 
that surrounds it measures the tendency of that metal 
to become oxidized by the au\ If this is so, and if (as 
is the case) the air is a bad conductor while the metals 
are good conductors, it ought to follow that when two 
different metals touch they equalize their own potentials 
by conduction but leave the films of air that surround 
them at different potentials. All the exact experiments 
yet made have measured the difference of potentials not 
between the metals themselves, but between the air near 
one metal and that near another metal. It is certain 
that while in ah' iron is positive to copper, but in an 
atmosphere of sulphuretted hydrogen, iron is negative to 
copper. Mr. John Brown has lately demonstrated the 
existence on freshly-cleaned metal surfaces of flms of 
liquid or condensed gases, and has shown that polished 
zinc and copper, when brought so near that their films 
touch, will act as a battery. 

81. Contact Actions. — A difference of potential is 
also produced by the contact of two dissimilar liquids with 
one another. 

* For the definition of the volt, or unit of diflference of potential, see 
Art. 254. 



CHAP. I CONTACT ACTIONS 87 

A liquid and a metal in contact with one another also 
exhibit a difference of xootential, and if the metal tends 
to dissolve into the liquid chemically there will be an 
electromotive force acting from the metal toward the 
liquid. 

The thermo-electric difference of potential at a junc- 
tion of two metals is a true contact difference. It is 
measiu'ed by the amount of heat produced (see Peltier- 
effect, Art. 420) by passing a current of electricity in the 
reverse direction through the junction. 

A liot metal placed in contact with a cold piece of 
the same metal also produces a difference of potential, 
electrical separation taking place across the surface of 
contact. 

Lastly, it has been shown by Professor J. J. Thomson 
that the surface of contact between two non-conducting 
substances, such as sealing-wax and glass, is the seat of a 
permanent difference of potentials. 

82. Magneto-electricity. — Electric currents flowing 
along in whes can be obtained from magnets by moving 
closed conducting circuits in their neighbourhood. This 
source is dealt with in Art. 222, Lesson XVIII. 

83. Summary. — We have seen in the preceding 
paragraphs how^ almost all conceivable agencies may pro- 
duce electrification in bodies. The most important of 
these are friction, heat, chemical action, magnetism, and 
the contact of dissimilar substances. We noted that the 
production of electricity by friction depended largely 
upon the molecular condition of the surfaces. We may 
here add that the difference of potentials produced by 
contact of dissimilar substances also varies with the 
temperature and with the nature of the medium (air, 
vacuum, etc.) in which the experiments are made. 
Doubtless this source also depends upon the molecular 
conditions of dissimilar substances being different ; the 
particles at the surfaces being of different sizes and 
shapes, and vibrating with different velocities and with 



88 ELECTRICITY AND MAGNETISM part i 

different forces. There are (see Art. 10) good reasons 
for thinking that the electricity of friction is really due 
to electricity of contact, excited at successive portions of 
the surfaces as they are moved over one another. But of 
the molecular conditions of bodies which determine the 
production of electrification where they come into contact, 
little or nothing is yet known. 



CHAPTER II 



MAGNETISM 



Lesson YIII. — Magnetic Attraction and Repulsion 

84. Lodestones or Natural Magnets. — The name 
Magnet (Magnes Lapis) was given by the ancients to 
certain hard black stones found in various parts of the 
world, notably at Magnesia in Asia Minor, which pos- 
sessed the property of attracting to them small pieces 
of iron. This magic property, as they deemed it, made 
the magnet-stone famous ; but it was not until the tenth 
or twelfth century that such stones were discovered to 
have the still more remarkable property of pointing 
north and south when hung up by a thread. This prop- 
erty was turned to advantage in navigation, and from 
that time the magnet received the name of Lodestone* 
(or "leading-stone"). The natural magnet or lodestone 
is an ore of kon, known to mineralogists as magnetite and 
having the chemical composition Fe304. This ore is 
found in quantities in Sweden, Spain, the Isle of Elba, 
Arkansas, and other parts of the world, though not 
always in the magnetic condition. It frequently occurs 
in crystals ; the usual form being the regular octahedron. 

85. Artificial Magnets. — If apiece of hard u'on be 
rubbed with a lodestone, it will be found to have also 

* The common spelling load&tone is due to misapprehension. 




Figs. 53 and 54. 



90 ELECTRICITY AND MAGNETISM part i 

acquired the properties characteristic of the stone ; it 
will attract light bits of iron, and if hung up by a 

thread it will point 
north and south. 
Savery, in 1729, 
first showed how 
much more reten- 
tive of magnetism 
hardened steel is 
than mere iron. 
Figs. 53 and 54 
represent a natural 
lodestone and an artificial magnet of steel, each of which 
has been dipped into iron-filings ; the filings are attracted 
and adhere in tufts. 

86. Writings of Dr. Gilbert. — This was all, or nearly 
all, that was known of the magnet until 1600, when 
Dr. Gilbert published a large number of magnetic dis- 
coveries in his famous work De Magnete. He observed 
that the attractive power of a magnet appears to reside 
at two regions, and in a long-shaped magnet these 
regions, or poles, are usually 'at the ends (see Figs. 53 
and 54). The portion of the magnet which lies between 
the two poles is apparently less magnetic, and does not 
attract iron-filings so strongly; and all round the mag- 
net, halfway between the poles, there is no attraction 
at all. This region Gilbert called the equator of the 
magnet, and the imaginary line joining the poles he 
termed the axis. 

87. Magnetic Needle. — To investigate more fully 
the magnetic forces a magnetic needle is employed. 
This consists (Fig. 55) of a light needle cut out of steel, 
and fitted with a little cap of brass, glass, or agate, by 
means of which it can be hung upon a sharp point, so 
as to turn with very little friction. It is rendered 
magnetic by being rubbed upon a magnet ; and when 
thus magnetized it will turn into the north-and-south 



MAGNETIC ATTRACTIONS 



91 



position, or, as ^ve should say, will set itself in the 



'-magnetic meridian 
by opticians consists 
of such a needle 
balanced above a 
card marked with 
"points of the com- 
pass." 

88. Magnetic 
Attractions and 
Repulsions. — If 
we take a magnet 
(either natural or 
artificial) in our 
hand and present 
the two " poles " of 
it successively to the 
north-pointing end 
of a magnetic needle, 
we shall observe that 



(Art. 151), 



The compass sold 




Fig. 55. 



one pole of the magnet attracts it, while the other repels 
it (Fig. 56). Repeating the experiment on the south- 
pointing end of 
the magnetic 
needle, we find 
that it is repelled 
by one pole and 
attracted by the 
other; and that 
the same pole 
which attracts the 
north-pointing 
end of the needle 
repels the south- 
pointing end. 
If we try a similar experiment on the magnetic 
needle, using for a magnet a second magnetized needle 




Fig. 56. 



92 ELECTRICITY AND MAGNETISM part i 

which has previously been suspended, and which has its 
north-pointing end marked to distinguish it from the 
south-pointing end, we shall discover that the N-pointing 
pole repels the N-pointing pole, and that the S-pointing 
pole repels the S-pointing pole ; but that a N-pointing pole 
attracts and is attracted by a S-pointing pole. 

89. Two Kinds of Magnetic Poles. — There would 
therefore appear to be two opposite kinds of magnetism, 
or at any rate two opposite kinds of magnetic poles, 
which attract or repel one another in very much the 
same fashion as the two opposite kinds of electrification 
do ; and one of these kinds of magnetism appears to have 
a tendency to move toward the north and the other to 
move toward the south. It has been proposed to call 
these two kinds of magnetism " north-seeking magnet- 
ism " and " south-seeking magnetism," but for our pur- 
pose it is sufficient to distinguish between the two kinds 
of poles. In common parlance the poles of a magnet are 
caUed the " North Pole " and " South Pole " respectively, 
and it is usual for the makers of magnets to mark the 
N-pointing pole with a letter N. It is therefore some- 
times called the " marked " pole, to distinguish it from 
the S-pointing or "unmarked " pole. We shall, to avoid 
any doubt,* call that pole of a magnet which would, 

* It is necessary to be precise on this point, as there is some confusion 
in the existing text-books. The cause of the confusion is this : — If the 
north-pointing pole of a needle is attracted b}' magnetism residing near the 
North Pole of the earth, the law of attraction (that unlike poles attract) 
shows us that these two poles are really magnetically of opposite kinds. 
Which are we then to call north magnetism ? That which is at the N pole 
of the earth ? If so, we must say that the N-pointing pole of the needle 
contains south magnetism. And if we call that north magnetism which 
points to the north, then we must suppose the magnetic pole at the north 
pole of the earth to have south magnetism in it. In either case there is 
then a difficulty- The Chinese and the French caU the N-pointing pole of 
the needle a south pole, and the S-pointing pole a north pole. Lord Kel- 
vin also calls the N-pointing pole a "True South" pole. But common 
practice goes the other way, and caUs the N-pointing pole of a magnet its 
" North " pole. For experimental purposes it is usual to paint the two 
poles of a magnet of different colours, the N-seeking pole being coloured 



CHAP. II POLAR EFFECTS 93 

if the magnet were suspended, tend to turn to the north, 
the " Xorth-seeking " pole, and the other the " South- 
seeking " pole. 

AVe may therefore sum up our observations in the con- 
cise statement: Like magnetic poles repel one another ; un- 
like poles attract one another. This Ave may call the first 
law of magnetism. As with the electric attractions and 
repulsions of rubbed bodies, so with these magnetic 
attractions and repulsions the effects are due, as we shall 
see, to stresses in the intervening medium. 

90. The two Poles inseparable. — It is impossible to 
obtain a magnet with only one pole. If we magnetize 
a piece of steel wire, or watch spring, by rubbing it with 
one pole of a magnet, we shall find that still it has two 
poles — one X-seeking, the other S-seeking. And if we 
break it into two parts, each part will still have two poles 
of opposite kinds. 

91. Magnetic Force. — The force with which a mag- 
net attracts or repels another magnet, or any piece of 
iron or steel, we shall caU magnetic force.* The force 
exerted by a magnet upon a bit 
of iron or on another magnet is 
not the same at all distances, the 
force being greater when the 
magnet is nearer, and less when 
the magiiet is farther off. (See 
Art. 128, on laws of magnetic -^. ^„ 

' ^ Fig. 5T. 

force.) 

Whenever a force acts thus between two bodies, it acts 
on both of them, tending to move both. A magnet will 
attract a piece of iron, and a piece of iron will attract 
a magnet. This was shown by Sir Isaac Xewton, who 

red and the S-seeking pole blue; but here again, strangely enough, 
authorities differ, for in the collections of apparatus at the Royal Institu- 
tion and Eoyal School of Mines, the colours are used in exactly the opposite 
way to this, which is due to Airy. 

* See footnote on "Force," Art. 169. 




94 ELECTRICITY AND MAGNETISM part i 

fixed a magnet upon a piece of cork and floated it in a 
basin of water (Fig. 57), and found that it moved across 
the basin when a piece of iron was held near. A com- 
pass needle thus floated turns round and points north 
and south ; but it does not rush towards the north as a 
whole, nor towards the south. The reason of this will 
be explained later, in Art. 129. 

Gilbert suggested that the force of a magnet might be 
measured by making it attract a piece of iron hung to 
one arm of a balance, weights being placed in the scale- 
pan hanging to the other arm; and he found, by hanging 
the magnet to the balance and placing the iron beneath 
it, that the effect produced was the same. The action 
and reaction are then equal for magnetic forces. 

92. Magnetic Substances. — A distinction was drawn 
by Gilbert between magnets and magnetic substances. A 
magnet attracts only at its poles, and they possess oppo- 
site properties. But a lump of iron will attract either 
pole of the magnet, no matter what part of the lump be 
presented to the magnet. It has no distinguishable 
fixed " poles," and no magnetic " equator." A true mag- 
net has poles, one of which is repelled by the pole of 
another magnet. 

93. Other Magnetic Metals. — Later experimenters 
have extended the list of substances which are attracted 
by a magnet. In addition to iron (and steel) the follow- 
ing metals are recognized as magnetic : — 

Nickel. Chromium. 

Cobalt. Cerium, 

and a few others. But only nickel and cobalt are at all 
comparable with iron and steel in magnetic power, and 
even they are very far inferior. Other bodies, sundry 
salts of iron and other metals, paper, porcelain, and 
oxygen gas, are also very feebly attracted by a powerful 
magnet.* 



CHAP. II IXDUCTIOK OF MAGNETISM 95 

94. Diamagnetism. — A number of bodies, notably 
bismuth, antimony, phosphorus, and copper, are appar- 
ently repelled from the poles of a magnet. Such bodies 
are called cUamagnetic bodies; a fuller account of them 
Tvill be found in Lesson XXIX. 

95. The Earth a Magnet. — The greatest of Gilbert's 
discoveries was that of the inherent magnetism of the 
earth. The earth is itself a great magnet, whose "poles" 
coincide nearly, but not quite, with the geographical 
north and south poles, and therefore it causes a freely- 
suspended magnet to tarn into a north-and-south posi- 
tion. Gilbert had some lodestones cut to the shape of 
spheres to serve as models of the globe of the earth. 
Such a globular magnet he called a terrella. He found 
that small magnets turned toward the poles of the ter- 
rella, and dip, as compass-needles do, toward the earth. 

The subject of Terrestrial Magnetism is treated of in 
Lesson XII. It is evident from the first law of magnet- 
ism that the magnetic condition of the northern regions 
of the earth must be the opposite to that of the north- 
seeking pole of a magnetized needle. Hence arises the 
difficulty alluded to on page 92. 

96. Induction of Magnetism. — Magnetism may be 
communicated to a piece of iron without actual contact 



Fig. 58. 

with a magnet. If a short, thin unmagnetized bar of 
iron be placed near some iron filings, and a magnet be 
brought near to the bar, the presence of the magnet will 
induce magnetism in the iron bar, and it will now attract 
the iron filings (Fig. 58). This inductive action is very 
similar to that observed in Lesson III. to take place when 
a non-electrified body was brought under the influence of 



96 ELECTRICITY AXD MAGNETISM part i 

an electrified one. The analogy, indeed, goes f mother 
than this, for it is found that the iron bar thus magnet- 
ized by induction vriU have two poles ; the pole nearest 
to the pole of the inducing magnet bemg of the opposite 
kind, Tvhile the pole at the farther end of the" bar is 
of the same kind as the inducing pole. Those bodies 
in -^hich a magnetizing force produces a high degree of 
magnetization are said to possess a high, permeability. It 
will be shoTvn presently that magnetic induction takes 
place along certain directions called lines of magnetic in- 
duction, or lines of magnetic force, which may pass either 
through iron and other magnetic media, or tki'ough air, 
vacuum, glass, or other non-magnetic media : and, since 
induction goes on most freely in bodies of high magnetic 
permeability, the magnetic lines are sometimes (though 
not too accurately) said to "pass by preference through 
magnetic matter," or, that "magnetic matter conducts 
the lines of force." 

97. Attraction across Bodies. — If a sheet of glass, 
or wood, or paper, be interposed between a magnet and 
the piece of ii'on or steel it is attracting, it will stiU at- 
tract it as if nothing were interposed. A magnet sealed 
up in a glass tube still acts as a magnet. Lucretius found 
a magnet put into a brass vase attracted iron filings 
through the brass. Gilbert surrounded a magnet by a 
ring of flames, and found it still to be subject to magnetic 
attraction from without. Across water, vacuum, and all 
known substances, the magnetic forces will act ; with the 
single apparent exception, however, that magnetic force 
will not act across a screen of iron or other magnetic 
material, if sufficiently thick. If a small magnet is sus- 
pended inside a hollow ball made of ii'on, no outside 
magnet will affect it. The reason being that the mag- 
netic lines of force are conducted off laterally through 
the iron instead of penetrating through it. A hollow 
shell of iron will therefore act as a magnetic cage, and 
shield the space inside it from magnetic influences. 



MAGNETIC SCREENING 



97 



Fig. 59 illustrates the way in which a cylinder of soft 
iron shields the space interior to it from the influence of 
an external magnet. A compass needle placed at P inside 
the cylinder is not affected by the presence of the magnet 
outside, for its lines of magnetic force are drawn off 
laterally. Similarly a magnet inside is shielded from 
affecting outside space. 

Although magnetic induction takes place at a distance 
across an intervening layer of air, glass, or vacuum, there 
is no doubt that the intervening medium is directly con- 
cerned in the transmission of the magnetic force, though 
the true medium is probably the " ether " of space sur- 




Fig. 59. 



rounding the molecules of matter, not the molecules 
themselves. 

We now can see why a magnet should attract a not- 
previously-magnetized piece of iron ; it first magnetizes 
it by induction and then attracts it : for the nearest end 
will have the opposite kind of magnetism induced in it, 
and will be attracted with a force exceeding that with 
which the more distant end is repelled. But induction 
precedes attraction. 

98- Retention of Magnetization. — Not all magnetic 
substances can become magnets permanently. Lode- 
stone, steel, and nickel retain permanently the great 
part of the magnetism imparted to them. Cast iron 
and many impure qualities of wrought iron also retain 

H 



98 ELECTRICITY AND MAGNETISM part i 

magnetism imperfectly. The softer and purer a speci- 
men of iron is, the more lightly is its residual magnet- 
ism retained. The following experiment illustrates the 
matter : — Let a few pieces of iron rod, or a few soft 
iron nails be taken. If one of these (see Fig. 60) be 
placed in contact with the pole of a permanent steel 
magnet, it is attracted to it, and becomes itself a tempo- 
rary magnet. Another bit of iron may then be hung 
to it, and another, until a chain of four or five pieces is 
built up. But if the steel mag- 
net be removed from the top of 
the chain, all the rest drop off, 
and are found to be no longer 
magnetic. A similar chain of 
steel needles may be formed, but 
they will retain permanently 
most of their magnetism. 

It will be found, however, that 
a steel needle is more difficult to 
magnetize than an iron needle 
^^o- ^^- of the same dimensions. It is 

harder to get the magnetism into steel than into iron, 
and it is harder to get the magnetism out of steel than 
out of iron ; for the steel retains the magnetism once 
put into it. This power of resisting magnetization, or 
demagnetization, is sometimes called coercive force; a 
much better term, due to Lamont, is retentivity. The 
retentivity of hard-tempered steel is great ; that of soft 
wrought iron is very smaU. The harder the steel, the 
greater its retentivity. Form affects retentivity. Elon- 
gated forms and those shaped as closed or nearly closed 
cu'cuits retain their magnetism better than short rods, 
balls, or cubes. 

99. Theories of Magnetism. — The student will not 
have failed to observe the striking analogies between 
the phenomena of attraction, repulsion, induction, etc., 
of magnetism and those of electricity. Yet the two sets 




CHAP. II METHODS OF MAGNETIZATION 99 

of phenomena are qnite distinct. A positively electrified 
body does not attract either the North-pointing or the 
South-pointing pole of the magnet as such ; in fact, it 
attracts either pole quite irrespective of its magnetism, 
just as it will attract any other body. There does exist, 
indeed, a direct relation between magnets and currents 
of electricity, as will be later explained. There is none 
known, however, between magnets and stationary charges 
of electricity. 

In many treatises it is the fashion to s^Deak of a mag- 
netic fluid or fluids ; it is, however, absolutely certain that 
magnetism is not a fluid, whatever else it may be. The 
term is a relic of bygone times. A magnet when rubbed 
upon a piece of steel magnetizes it without giving up or 
losing any of its own magnetism. A fluid cannot possibly 
propagate itself indefinitely without loss. The arguments 
to be derived from the behaviour of a magnet on breaking, 
and from other experiments narrated in Lesson X., are 
even stronger. N'o theory of magnetism will therefore 
be propounded until these facts have been placed before 
the student. 



Lesson IX. — Methods of making Magnets 

100. Magnetization by Single Touch. — It has been 
so far assumed that bars or needles of steel were to be 
magnetized by simply touching them, or stroking them 
from end to end with the pole of a permanent magnet of 
lodestone or steel. In this case the last touched point of 
the bar will be a pole of opposite kind to that used to touch 
it ; and a more certain effect is produced if one pole of 
the magnet be rubbed on one end of the steel needle, and 
the other pole upon the other end. There are, however, 
better ways of magnetizing a bar or needle. 

101. Magnetization by Divided Touch. — In this 
method the bar to be magnetized is laid down hori- 




100 ELECTRICITY AND MAGNETISM part i 

zontally ; two bar magnets are then placed down upon 
it, their opposite poles being together. They are then 
drawn asunder from the middle of the bar towards its 
ends, and back, several times. 
The bar is then turned over, 
and the operation repeated, 
taking care to leave off at the 
Fig. Gi. middle (see Fig. 61). The 

process is more effectual if 
the ends of the bar are meantime supported on the poles 
of other bar magnets, the poles being of the same names 
as those of the two magnets above them used for strok- 
ing the steel bar. 

102. Magnetization by Double Touch. — Another 
method, known as double touch, differs slightly from that 
last described. A piece of wood or cork is interposed 
between the ends of the two bar magnets employed, and 
they are then both moved backwards and forwards along 
the bar that is to be magnetized. By none of these 
methods, however, can a steel bar be magnetized beyond 
a certain degree of intensity. 

103. Forms of Magnets. — Natural magnets are usu- 
ally of irregular form, though they are sometimes reduced 
to regular shapes by cutting or grinding. Formerly it 
was the fashion to mount them with soft iron cheeks or 
" armatures " to serve as pole-pieces. 

For scientific experiments bar magnets of hardened 
steel are commonly used ; but for many purposes the 
horse-shoe shape is preferred. In the horse-shoe magnet 
the poles are bent round so as to approach one another, 
the advantage here being that so both poles can attract 
one piece of iron. The " armature," or " keeper," as the 
piece of soft iron placed across the poles is named, is 
itself rendered a magnet by induction when placed across 
the poles ; hence, when both poles magnetize it, the force 
with which it is attracted to the magnet is the greater. 

104. Laminated Magnets. — It is found that long 



CHAP. II LAMINATED MAGNETS 101 

thin steel magnets are more powerful in proportion to 
their weight than thicker ones. Hence it was proposed 
by Scoresby* to construct compound magnets, consisting 
of thin laminae of steel separately magnetized, and after- 




Fig. 62. 



w^ards bound together in bundles (Fig. 62). These 
laminated magnets are more powerful than simple bars 
of steel. Compound horse-shoe magnets are sometimes 
used : the plates separately magnetized are assembled as 
in Fig. 63. 

105. Magnetization derived from the Earth. — The 
magnetism of the earth may be utilized where no other 
permanent magnet is available to magnetize a bar of 
steel. Gilbert states that iron bars set upright for a 
long time acquire magnetism from the earth. If a steel 
poker be held in the magnetic meridian, with the north 
end dipping down, and in this position be struck with 
a wooden mallet, it will be found to have acquired 
magnetic properties. All vertical iron columns in our 
northern latitudes are found to have their lower ends 
K poles and their upper ends S poles. In Australia and 
the southern hemisphere the tops of iron columns are 
X poles. Wires of steel subjected to torsion, while in 
the magnetic meridian, are also found to be thereby 
magnetized. 

106. Magnetization after Heating. — Gilbert discov- 
ered also that if a bar of steel be heated to redness, and 
cooled, either slowly or suddenly, while lying in the 
magnetic meridian, it acquires magnetic polarity. Ko 

* A similar suggestion was made by Geuns of Venlo in 1T6S, using 
horse-shoe magnets. Similar magnets have been constructed in recent 
years by Jamin. 



102 ELECTEICITY AXD MAGXETISM part i 

such property is acquired if it is cooled -while lying east 
and west. It has been proposed to make powerful mag- 
nets by placing hot bars of steel to cool between the 
poles of very powerful electromagnets; and Carre pro- 
duced strong magnets of iron cast in moulds lying in an 
intense magnetic field. 

107. Magnetization by Currents of Electricity. — A 
current of electricity caused to circulate in a spiral wire 
wound around a core of iron or steel magnetizes it more 
powerfully than in any of the preceding operations. 

In the case of a soft iron core, it is 
i f==— --Hl^i only a magnet while the current con- 

^^^^L__^^===" tinues to flow. Such a combination is 
^^^^^B termed an Electromagnet; it is fully 

^^^^^MB^ described in Lesson XXXI. Fig. 6i 

^^^^^^^ depicts a common form of electro- 

^:~^zI^ZIir~A magnet having two coils of insulated 

"^-^JiSlIP copper wire wound upon bobbins that 

Fi". 64. ^^'6 placed upon the limbs of a soft 

iron core. The armature is also of 
soft iron of sufficient thickness. Steel bars may be mag- 
netized by drawing them over the poles of such an 
electromagnet while the latter is excited by the circula- 
tion of the electric current. Elias of Haarlem proposed 
to magnetize steel bars by passing them through a wire 
coiled up into a compact ring of many turns, through 
which a strong current was sent by a voltaic battery. 

108. Hardening and Tempering of Steel for Mag- 
nets. — There are two ways of hardening steel: (1) by 
suddenly cooling it from a bright red temperature; 
(2) by compressing it under hydraulic pressure while it 
cools slowly. If rods of steel are heated brilliantly red, 
and then quenched in water, oil, or mercury, they become 
intensely brittle and glassy-liar d. To temper hard steel 
it is then gently reheated to near a very dull red heat 
and softens slightly while acquiring a straw tint. If let 
down still further by continuing the reheating it becomes 



CHAP. II UNVARYING MAGNETS 103 

a blue tint, and is springy and flexible. Short bar mag- 
nets retain most magnetism if left glass-hard without 
tempering. But magnets whose length is more than 
twenty times their thickness retain more magnetism if 
tempered down to a straw or even to a blue tint, 

109 . Destruction of Magnetism. — A steel m agnet loses 
its magnetism partially or wholly if subjected to rough 
usage, or if purposely hit or knocked about. I^J'ewly mag- 
netized magiiets lose more strength by rough treatment 
than those which have been long magnetized. A magnet 
loses its magnetism, as Gilbert showed, on being raised 
to a bright red-heat. The slightest vibration will de- 
stroy any magnetism remaining in annealed soft iron. 

110. Magnets of Unvarying Strength. — Ordinary steel 
magnets have by no means a permanent or constant mag- 
netism. They soon lose a considerable percentage of 
their magnetism, and the decay continues slowly for 
months and years. Every shock or jolt to which they 
are subjected, every contact with iron, every change of 
temperature weakens them. Every time that the keeper 
is slammed on to a horse-shoe magnet it is weakened. 
For the purpose of making magnetic measurements, and 
for use as controlling magnets of galvanometers, magnets 
are, how^ever, required that shall possess the utmost con- 
stancy in their strength. Magnets of unvarying strength 
may be made by attention to following points. Choose 
a form either of a nearly closed circuit or of a very long- 
rod. Let the steel be hardened as much as possible (see 
Art. 108 above), then placed in steam at 100° for twenty 
or thirty hours or more. Then magnetize as fully as 
possible, and then heat again for five hours in steam. 
Magnets of a shape constituting a nearly closed circuit 
are more constant than short straight magnets. 

111. Effects of Heat on Magnetization. — If a perma- 
nent steel magnet be w^armed by placing it in hot or boil- 
ing water, its strength will be thereby lessened, though 
it recovers partially on cooling. Chilling a magnet in- 



104 ELECTRICITY AND MAGNETISM part i 

creases its strength. Cast iron ceases to be attracted by 
a magnet at a bright red-heat, or at a temperature of 
about 700° C. Cobalt retains its magnetism at the high- 
est temperatures. Chromium ceases to be magnetic at 
about 500° C, and nickel at 350° C. Manganese ex- 
hibits magnetic attraction only when cooled to — 20° C. 
It has therefore been surmised that other metals would 
also become magnetic if cooled to a low enough tempera- 
ture. Trowbridge found severe cooling to 100° below 
zero to destroy the magnetism of steel magnets ; but 
Dewar has observed that when cooled to near — 200° C. 
in liquid oxygen the magnetic properties of iron are 
nearly twice as high as at 0° C. The magnetic metals at 
high temperatures do not become diamagnetic, but are 
still feebly magnetic. 

112. Magnetic Saturation. — A magnet to which as 
powerful a degree of magnetization as it can attain to has 
been given is said to be saturated. A recently magnetized 
magnet will occasionally appear to be super-saturated, pos- 
sessing even after the application of the magnetizing force 
has ceased a higher degree of magnetism, than it is able 
to retain permanently. Thus a horse-shoe-shaped steel 
magnet will support a greater weight immediately after 
being magnetized than it will do after its armature has 
been once removed from its poles. Even soft iron after 
being magnetized retains a small amount of magnetism 
when its temporary magnetism has disappeared. This 
small remaining magnetic charge is spoken of as residual 
magnetism. 

113. Strength of a Magnet. — The "strength" of a 
magnet is not the same thing as its " lifting power." Its 
lifting power is a very uncertain quantity depending not 
only on the shape of its polar surfaces, but on the shape 
and quality of the mass of iron used as load. Conse- 
quently the " strength " of a magnet pole must be meas- 
ured by the magnetic force which it exerts at a distance 
on other magnets. Thus, suppose there are two magnets, 



CHAP. II LIFTING POWER 105 

A and B, whose strengths we compare by making them 
each act upon the X pole of a thh'd magnet C. If the I*^ 
pole of A repels C with twice as much force as that with 
which the X pole of B placed at the same distance would 
repel C, then we should say that the '• strength " of A was 
twice that of B. Another way of putting the matter is 
to say that the " strength " of a pole is the amount of free 
magnetism at that pole. By adopting the unit of strength 
of magnet poles as defined in Art. 141, we can express 
the strength of any pole in numbers as so many " units " 
of strength. 

114. Lifting Power. — The lifting power of a magnet 
(also called its portative force) depends both upon the 
form of the magnet and on its magnetic strength. A 
horse-shoe magnet will lift a load three or four times as 
gTeat as a bar magnet of the same weight will lift. A 
long bar magnet will lift more than a short bar magnet 
of equal strength. A bar magnet with a rounded or 
chamfered end will lift more than a similar bar with a 
flat or expanded end, though both may be equally 
strongly magnetized. Also the lifting power of a mag- 
net grows in a very curious and unexplained way by 
gradually increasing the load on its armature day by 
day until it bears a load w^hich at the outset it could not 
have done. Nevertheless, if the load is so increased that 
the armature is torn off, the power of the magnet falls 
at once to its original value. The attraction between a 
powerful electromagnet and its armature may amount to 
200 lbs. per square inch, or 14,000 grammes per square 
centimetre (see Art. 384), Small magnets lift a greater 
load in proportion to their own weight than large ones,* 
because the lifting power is proportional to the polar 

* Bernoulli gave the following rule for finding the lifting power p of 
a magnet whose weight was w : — 

3 

p z=aVio ; 

where a is a constant depending on the goodness of the steel and the 



106 ELECTRICITY AND MAGNETISM part i 

surface, other things being equal. Steel magnets sel- 
dom attain a tractive force as great as 40 lbs. per square 
inch of polar surface. A good steel horse-shoe magnet 
weighing itself 1 lb, ought to lift 25 lbs. weight. Sir 
Isaac Xewton is said to have possessed a little lodestone 
mounted in a signet ring which would lift a piece of iron 
200 times its own weight. 



Lessox X. — Distribution of Magnetism 

115. Magnetic Field. — The space all round a magnet 
pervaded by the magnetic forces is termed the ^'- field'" of that 
magnet. It is most intense near the poles of the magnet, 
and is weaker and weaker at greater distances away. At 
every point in a magnetic field the force has a particular 
strength, and acts in a particular direction. It is pos- 
sible at any point in a magnetic field to draw a line in 
the direction of the resultant magnetic force acting at that 
point. The whole field may in this way be mapped out 
with magnetic lines (Art. 119). For a horse-shoe magnet 
the field is most intense between the two poles, and the 
lines of magnetic force are curves which pass from 
one pole to the other across the field. A practical way 
of investigating the distribution of the magnetic lines 
in a field is given in Art. 119, under the title " Mag- 
netic Figures." When the armature is placed upon the 
poles of a horse-shoe magnet, the force of the magnet on 
all the external regions is weakened, for the induction 
now goes on through the iron of the keeper, not through 
the surrounding space. In fact a closed system of magnets 
— such as that made by placing four bar magnets along 
the sides of a square, the X pole of one touching the S 

method of magnetizing it. In the best steel magnets made at Haarlem 
by Yan Wetteren this coefficient was from 19-5 to 23, the weights being ex- 
pressed in kilogrammes. 



BKEAKING A MAGNET 



107 



pole of the next — has no external field of force. A ring 
of steel may thus be magnetized so as to have neither 
external field nor poles ; or rather any point in it may 
be regarded as a X pole and a S pole, so close together 
that they neutralize one another's forces. 

That poles of opposite name do neutralize one another 
may be sho"\^ai by the well-known experiment of hanging 
a small object — a steel ring or a key — to the i^ pole of 
a bar magnet. If now the S pole of another bar magnet 
be made to touch the first the two poles will neutralize 
each other's actions, and the ring or key will drop down. 

116. Breaking a Magnet. — We have already stated 
that when a magnet is broken into two or more parts, 
each is a complete magnet, possessing poles, and each is 
nearly as strongly magnetized as the original magnet. 



m 






m. 



— S>lN^Si^ ^liillillillllllillillllillill 
Fig. 65. 

Fig. 65 shows this. If the broken parts be closely joined 
these adjacent poles neutralize one another and disappear, 
leavmg only the poles at the ends as before. If a magnet 
be ground to powder each fragment wiU still act as a 



N 



S'N' 



n H 


;/ .x 


n 


—? 


n ,s 


n 


~ 


— 


— 


n- 


— 


w- 


-s 


n s 


n 


s 


a 


s 


n s 


n 


•s 


V 


s 


n 


s 


n 


s 


a H 


n 


•s 


n 


s 


n s 


n 


,9 


n s 


n 


s 


11 


s 


n s 


n 


•^ 


n ,s 


.1 s 


H 


.i 


n 


s 


n 


s 


n 


s 


N 










s 

Fig. 


66. 














s 



little magnet and exhibit polarity. A magnet may there- 
fore be regarded as composed of many little magnets put 
together, so that their like poles all face one way. Such 
an arrangement is indicated in Fig. 66, from which it 
will be seen that if the mag-net be broken asunder across 



108 ELECTRICITY AND MAGNETISM part i 

any part, one face of the fracture will present only X 
poles, the other only S poles. This would be true no 
matter how small the individual particles. 

117. Normal Distribution. — In an ordinary bar mag- 
net the poles are not quite at the ends of the bar, but 
a little way from it ; and it can be shown that this is 
a result of the way in which the surface magnetism is 
distributed in the bar. A very long, thin, uniformly 
magnetized bar has its poles at the ends ; but in ordinary 
thick magnets the "pole " occupies a considerable region, 
the "fi-ee magnetism" falling off gradually from the 
ends of the bar. In each region, however, a point can 
be generally determined at which the resultant magnetic 
forces act, and which may for most pm-poses be considered 
as the "pole." In certain cases of iiTegular magnetiza- 
tion it is possible to have one or more poles between 
those at the ends. Such poles are called consequent poles 
(see Fig. 70). 

118. Lamellar Distribution of Magnetism. Magnetic 
Shells. — Up to this point the ordinary disti'ibution of 
magnetism along a bar has been the only distribution 
considered. It is theoretically possible to have magnet- 
ism distributed over a thin sheet so that the whole of 
one face of the sheet shall have one kind of magnetism, 
and the other face the other kind of magnetism; such 
distribution is, however, unstable. If an immense num- 
ber of little magnets were placed together side by side, 
like the cells in a honeycomb, all with their ^-seeking 
ends upwards, and S-seeking ends do^mwards, the whole 
of one face of the slab would be one large flat X-seeking 
pole, and the other face S-seeking. Such a distribution 
as this over a surface or sheet is termed a lamellar dis- 
tribution, to distinguish it from the ordinary distribu- 
tion along a line or bar, which is termed, for distinction, 
the solenoidal, or circuital, distribution. A lamellarly 
magnetized magnet is sometimes spoken of as a magnetic 
shell. 



MAGNETIC FIGURES 



109 



119. Magnetic Figures. — Gilbert showed * tha,t if a 
sheet of paper or card be placed over a magnet, and iron 
filings are dusted over the paper, they settle down in 
curving lines, forming a magnetic figure, the general form 
of which for a bar magnet is shown in Fig. 67. The 
filings should be fine, and sifted through a bit of muslin ; 
to facilitate their settling in the lines, the sheet of paper 
should be lightly tapped. The figures thus obtained can 
be fixed permanently by several processes. The best of 
these consists in employing a sheet of glass which has 




Fig. 67. 



been previously gummed and dried, instead of the sheet 
of paper ; after this has been placed above the magnet 
the filings are sifted evenly over the surface, and then 
the glass is tapped ; then a jet of steam is caused to play 
gently above the sheet, softening the surface of the gum, 
which, as it hardens, fixes the filings in their places. In- 
spection of the figure will show that the lines diverge 
nearly radially from each pole, and curve round to meet 
these from the opposite pole. Fig. 68, produced from a 
horse-shoe magnet, shows how the magnetic field is most 

* The magnetic figures were known to Lucretius. 



110 



ELECTEICITY AND MAGNETISM part i 



intense between the poles, but spreads beyond them in 

wide curves. Faraday, who made a great use of this 

niethod of investigating 
the distribution of mag- 
netism in various "fields," 
gave to the lines the name 
of lines of force. They 
represent, as shown by the 
action on little magnetic 
particles which set them- 
selves thus in obedience to 
the attractions and repul- 
sions in the field, the re- 
sultant direction of the 
forces at every point ; for 
each particle tends to as- 
sume the direction of the 
force jointly due to the 
simultaneous action of 

both poles ; hence the curves of filings may be taken to 

represent visibly the in- 
visible lines of rnagnetic 

force.* Faraday pointed out 

that these " lines of force " 

map out the magnetic field, 

showing by their position the 

direction of the magnetic 

force, and by their number 

its intensity. If a sm.all N"- 

seeking pole could be obtained 

alone, and put down on any 

one of these lines of force, it 

would tend to move along 

that line from N to S; a single S-seeking pole would 

* Or rather the component part of the magnetic force resolved into the 
plane of the figure ; -which is not quite the same thing, for above the poles 
the filings stand up nearly vertically to this plane. 





CHAP. II CONSEQUENT POLES 111 

tend to move along the line in an o^Dposite direction. In 
Fig. 69, which is the field about one end of a bar magnet, 
the magnetic lines are simply radial. Faraday also 
pointed out that the actions of attraction or repulsion 
in the field are always related to the directions in the 
field of the magnetic lines. He assigned to these lines of 
force certain physical properties (which are, however, only 
true of them in a secondary sense), viz. that they tend to 
shorten themselves from end to end, and that they repel 
one another as they lie side by side. The modern way 
of stating the matter is, that in every magnetic field 
there are certain stresses, consisting of a tension along 
the lines of force, and a pressure across them. 

120. Consequent Poles. — The method of sprinkling 
filings may be applied to ascertain the presence of conse- 




Fig. 70. 

quent poles in a bar of steel, the figure obtained resem- 
bling that depicted in Fig. 70. Such a state of things is 
produced when a strip of very hard steel is purposely 
irregularly magnetized by touching it with strong mag- 
nets at certain points. A strip thus magnetized virtually 
consists of several magnets put end to end, but in reverse 
directions, NS, SN, etc. Consequent poles can also be 
produced in an electromagnet by reversing the direction 
in which the wire is coiled around part of the core. 

121. Fields mapped by Filings. — The forces pro- 



112 



ELECTRICITY AND MAGNETISM part i 



ducing attraction between unlike poles, and repulsion 
between like poles, are beautifully illustrated by the 
magnetic figiu'es obtained in the fields between the poles 
in the two cases, as given in Figs. 71 and 72. In Fig. 71 
the poles are of opposite kinds, and the lines of force 
curve across out of one pole into the other; while in Fig. 




72, which represents the action of two similar poles, the 
lines of force cui've away as if repelling one another, and 
turn aside at right angles. 

122. Magnetic Writing. — Another kind of mag- 
netic figures was discovered by De Haldat, who wrote 
with the pole of a magnet upon a thin steel plate (such 
as a saw-blade), and then sprinkled filings over it. The 
writing, which is quite invisible in itself, comes out in 
the lines of filings that stick to the magnetized parts ; 
this magic writmg will continue in a steel plate many 
months. 

123. Surface Magnetization. — In many cases the 
magnetism imparted to magnets is confined chiefly to 
the outer layers of steel. If a short bar magnet be put 
into acid so that the outer layers are dissolved awaj', it 
is found that it has lost its magnetism when only a thin 
film has been thus removed. A short hollow steel tube 
when magnetized is nearly as strong a magnet as a solid 
rod of the same size. Long thin magnets, and those that 
are curved so as nearly to form a closed circuit can be 
much more thoroughly magnetized. If a bundle of steel 
plates are magnetized while bound together, it will be 



CHAP. II EFEECTS OF MAGNETIZATION 113 



found that only the outer ones are strongly magnetized. 
The mner ones may even exhibit a reversed magnetization. 
124. Mechanical Effects of Magnetization. — Joule 
found an n^on bar to increase by ^^^^^^ of its length 
when strongly magnetized. Bidwell found that with 
stiU stronger magnetizing forces iron contracts again- 
and rods stretched by a weight contract more when 
magnetized than unstretched rods do. Barrett observed 
that nickel shows a slight contraction when magnetized. 
These are proofs that magnetization is an action affecting 
the arrangement of the molecules. This supposition is 
confirmed by the observation of Page, that at the moment 
when a bar is magnetized or demagnetized, a faint metal- 
he clmk is heard in the bar. Sir W. Grove showed that 
when a tube containing water rendered muddy by stir- 
rmg up in it finely divided magnetic oxide of iron was 
magnetized, the liquid became clearer in the direction of 
magnetization the particles apparently setting themselves 
end-on, and allowing more light to pass between them. 
A twisted iron wire tends to untwist itself when magnet- 
ised. A piece of iron, when powerfully magnetized and 
demagnetized m rapid succession, grows hot, as if mag- 
netization were accompanied by internal friction 

125 Action of Magnetism on Light. - Faraday 
discovered that a ray of polarized light passing through 
certain substances in a powerful magnetic field has the 
direction of its vibrations changed. This phenomenon, 
which IS sometimes called " The Magnetization of Lio-ht " 
IS better described as "The Rotation of the Plane of 
Polarization of Light by Magnetism." The amount of 
rotation differs m different media, and varies with the 
magnetizing fo^ce. More recently Kerr has shown that 
a ray of polarized light is also rotated by reflexion at the 
end or side of a powerful magnet. Further mention is 
Le^sson LvF ''^''^' "' the chapter on Electro-optics, 

126. The Act of Magnetizing. -All these various 



11-1 



ELECTEICITY AND MAGNETISM part i 



phenomena point to a theory of magnetism very different 
from the old notion of fluids. It appears that every 
particle of a magnet is itself a magnet, and that the 
magnet only becomes a magnet as a whole by the parti- 
cles being so tiu-ned as to point one way. The act of 
magnetizing consists in turning the molecules more or less 
into one particular dn-ection. This conclusion is supx:>orted 
by the obserYation that if a 
glass tube full of iron filings 






:;^ir'\\-^ 



is magnetized, the filings can 
-IJv^T^ be seen to set themselves end- 
Pig. 73 ^ays, and that, when thus 

once set, they act as a mag- 
net until shaken up. It a]3pears to be harder to turn 
the individual molecules of solid steel than those of 
soft iron ; but. when once so set, they remain end-on 
unless violently struck or heated. As Weber, who pro- 
pounded this notion of molecular magTietism, pointed 
out, it follows from this theory that when all the particles 
are tm-ned end-on the limits of possible magnetization 
would have been 

attained. Some \ \ \ \ \^ ,- — ~.^ / / / ,' / 
careful experi- ^^"^^\^. \ \ :. ': ,-' y'//y'y 

ments of Beetz 
on iron deposited 
by electrolysis 

entirely confirm '/' /' / / ,' '\,. ^ \ '« \ \ \ 

this conclusion, ' ' Y\g. 74. 

and add weight 

to the theory. Fig. 73 may be taken to represent a non- 
magnetized piece of iron or steel in which the arrangement 
of the particles is absolutely miscellaneous : they do not 
point in any one direction more than another. "When 
magnetized slightly, there will be a gi-eater percentage 
pointing in the direction of the magnetizing force. When 
fully magnetized — if that were possible — they would all 
point in the same direction as in Fig. 7i. 



CHAP. II THEORY OF MAGNETIZATION 115 

In very few cases, however, is the magnetization 
uniform throughout the whole length of a bar : the 
particles are more fully completely turned into line at 
the middle part of the bar than at the ends. 

K the intrinsic magnetization of the steel at every 
part of a magnet were equal, the free poles would be 
found only at the end surfaces ; but the fact that the free 
magnetism is not at the ends merely, but diminishes from 
the ends towards the middle, shows that the intensity of 
the intrinsic magnetization must be less towards and 
at the ends than it is at the middle of the bar. In Fig. 
74 an attempt is made to depict this. It will be noticed 
that the magnetic lines run through the steel and emerge 
into the an- in cm-ves. Some of the lines do not run all 
the length of the bar but leak out at the sides. If the 
bar were uniformly magnetized the lines would emerge 
at the ends only. It is clear that the middle piece is 
more thoroughly magnetized than any other part. Mag- 
netism in fact consists of a sort of grain or structure con- 
ferred upon the steel. Wherever this structure conies up 
at a surface, there the surface properties of magnetism are 
found. A pole is simply a region where the magnetic 
lines pass through the surface of the steel or iron. 

The optical phenomena led Clerk Maxwell to the 
further conclusion that these longitudinally-set molecules 
are rotating round their long axes, and that in the " ether " 
of space there is also a vortical motion along the lines of 
magnetic induction ; this motion, if occurring in a perfect 
medium (as the " ether " may be considered), producing 
tensions along the lines of the magnetic field, and press- 
ui"es at right angles to them, would afford a satisfactory 
explanation of the magnetic attractions and repulsions 
which apparently act across empty space. 

Hughes, Barus, and others have lately shown that the 
magnetism of iron and steel is intimately connected with 
the molecular rigidity of the material. Hughes's re- 
searches with the " induction balance " (Art. 514) and 



116 ELECTRICITY AND MAGNETISM part i 

"magnetic balance " (Art. 140) tended to prove that each 
molecule of a magnetic metal has an absolutely constant 
inherent magnetic polarity ; and that when a piece of 
iron or steel is apparently neutral, its molecules are inter- 
nally arranged so as to satisfy each other's polarity, form- 
ing closed magnetic circuits amongst themselves. 

127. Ewing's Theory of Molecular Magnetism. — 
Weber supposed that there was in hard steel some sort 
of friction which prevented the molecules when once 
magnetized from turning back into higgledy-piggledy 
positions. Ewing, however, showed that a complete ex- 
planation was afforded by supposing the particles to be 
subject to mutual forces. In any group not subjected to 
an external magnetizing force the particles will arrange 
themselves so as to satisfy one another's polarity. Of the 



^ / , 


\ 


\ 




\~ 




-> 


— > 


\ / ^ 


\ ^ 


i< 


V 


\^ 


^ I 


\- 


- 1 


V/ 


A 


\ 




\ 


/ 


\ 


/ 



Fig. 75. 

possible gToupings some are, however, unstable. Four 
possible stable groupings of six pivoted needles are shown 
in Fig. 75. Ewing constructed a model consisting of a 
large number of pivoted magnetic needles arranged in 
one layer. When these needles were simply agitated and 
allowed to come to rest they settled down in miscellaneous 
groups ; but when acted upon by a gradually increasing 
magnetic force they turned round, the operation showing 
three stages — (i.) with very small magnetizing force the 
needles merely turned through a small angle ; (ii.) when 
a certain force was applied the groupings became unsta- 
ble, some of the needles suddenly swinging round to a new 
position, with the result that the majority of the needles 



CHAP. II LAWS OF MAGNETIC FORCE 117 

point nearly but not quite along the direction of the 
force ; (iii.) a further increase of the magnetizing force 
cannot produce much more effect ; it can only pull the 
needles a little more perfectly into line. All these things 
correspond to the three stages observed (see Art. 364) in 
the gradual magnetization of iron or steel. 



Lessox XI. — Laws of Magnetic Force 

128. Laws of Magnetic Force. 

First Law. — Like magnetic poles repel one 
another; unlike magnetic poles attract one 
another. 

Second Law. — The force exerted between two 
magnetic poles is proportional to the product 
of their strengths, and is inversely propor- 
tional to the square of the distance between 
them, provided that the distance is so great 
that the poles may be regarded as mere points. 

129. The Law of Inverse Squares. — The second 
of the above laws is commonly known as the law of 
inverse squares; it 

is essentially a law 
of point - action, 
and is not true for 
poles of elongated 
or extended sur- 
face. The similar 
law of electrical 
attraction has al- ^^e- ''*^- 

ready been explained and illustrated (Art. 19). This law 
furnishes the explanation of a fact mentioned in an earlier 
lesson, Art. 91, that small pieces of iron are drawn bodily 
up to a magnet pole. If a small piece of iron wire, a, b (Fig. 
76), be suspended by a thread, and the N-pointing pole 




118 ELECTRICITY AND MAGNETISM part i 

A of a magnet be brought near it, the iron is thereby in- 
ductively magnetized ; it turns round and points towards 
the magnet pole, setting itself as nearly as possible 
along a line of force, its near end & becoming a S-seeking 
pole, and its farther end a becoming a X-seeking pole. 
Now the pole 1) will be attracted and the pole a will be 
repelled. But these two forces do not exactly equal one 
another, since the distances are unequal. The repulsion 
will (by the law of inverse squares) be proportional to 

-—, ;; and the attraction will be proportional to ^ . ,. • 

(Aa)^ "■ ^ (A&)2 

Hence the bit of iron a, h will experience a pair of forces, 

turning it into a certain direction, and also a total force 

drawing it bodily toward A. Only those bodies are 

attracted by magnets in which magnetism can thus be 

induced; and they are attracted only because of the 

magnetism induced in them. 

We mentioned, Art. 91, that a magnet needle floating 
freely on a bit of cork on the surface of a liquid, is acted 
upon by forces that give it a certain direction, but that, 
unlike the last case, it does not tend to rush as a whole 
either to the north or to the south. It experiences a 
rotation, because the attraction and repulsion of the 
magnetic poles of the earth act in a certain direction; 
but since the magnetic poles of the earth are at a distance 
enormously great as compared with the length from one 
pole of the floating magnet to the other, we may say that, 
for all practical purposes, the poles of the magnet are at 
the same distance from the N pole of the earth. The 
attracting force on the N-pointing pole of the needle is 
therefore practically no greater than the repeUing force 
acting on the S-pointing pole, hence there is no motion 
of translation given to the floating needle as a whole : it 
is directed, not attracted. 

130. Measurement of Magnetic Forces. — The truth 
of the law of inverse squares can be demonstrated by 
experiment. But this implies that we have some means 



CHAP. II 



MEASUEEMENT OF FORCE 



119 



of measuring acciiratel}' the amount of the magnetic 
forces of attraction or repulsion. Magnetic force may be 
measured in any one of the four following ways : (1) by 
observing the time of swing of a magnetic needle oscil- 
lating under the influence of the force ; (2) by observing 
the deflexion it produces upon a magnetic needle which 
is already attracted into a different direction by a force 
of known intensity ; (3) by balancing it against the tor- 
sion of an elastic thread ; (4) by balancing it against the 
force of gTavity as brought into play in attempting to 
deflect a magnet hung by two parallel strings (called the 
hijilar suspension), for these strings cannot be twisted 
out of theii" parallel position without raising the centre 
of gravity of the magnet. 

131. Deflexion Experiment. — Fig. 77 shows an ap- 
paratus in which a compass-needle 

can be deflected by one pole of a 
magnet made of a long thin bar of 
steel, so mounted that its upper pole 
is always over the centre of the 
needle, and therefore has no tendency 
to turn it. So set, it acts as a one- 
pole magnet, the pole of which can 
be placed at different distances from 
the compass-needle. It is found, using 
a proper tangent-scale (see Art. 211) 
for the compass-needle, that when the 
distance is doubled the deflecting force is reduced to one 
quarter, and so forth. 

132. The Torsion Balance. — Coulomb applied the 
Torsion Balance to the measurement of magnetic forces. 
The main principles of this instrument (as used to meas- 
ure forces of electrostatic repulsion) were described on 
p. 20. Fig. 78 shows how it is arranged for measuring 
magnetic repulsions. 

To prove the law of inverse squares, Coulomb made the 
following experiment : — The instrument was first adjusted. 




120 



ELECTEICITY A^'D MAGNETISM part i 



so that a magnetic needle, hung in a coiDper stirrup to the 
fine silver thread, lay in the magnetic meridian without 
the wu-e being t\Yisted. This was done by first putting 
in the magnet and adjusting roughly, then replacing it by 
a copper bar of equal weight, and once more adjusting, 
thus diminishing the error by repeated trials. The next 




rig. TS. 

step was to ascertain through what number of degrees the 
torsion-head at the top of the thread must be twisted in 
order to di-ag the needle 1° out of the magnetic meridian. 
In the particular experiment cited it was found that 35° 
of torsion corresponded to the 1° of deviation of the 
magnet ; then a magnet was introduced through the lid, 
that pole being do^^-nwards which repelled the pole of the 



CHAP. II TORSION BALANCE 121 

suspended needle. It was found (in this particular ex- 
periment) to repel the pole of the needle through 24°. 
From the preliminary trial we know that this directive 
force corresponds to 24° x 35° of the torsion-head, and to 
this we must add the actual torsion on the Avire, viz. the 
24°, making a total of 864°, which we will call the 
" torsion equivalent " of the repelling force when the poles 
are thus 24° apart. Finally the torsion-head was turned 
round so as to twist the suspended magnet round, and 
force it nearer to the fixed pole, until the distance between 
the repelling poles was reduced to half what it was at 
first. It Avas found that the torsion-head had to be turned 
round 8 complete rotations to bring the poles to 12° apart. 
These 8 rotations were an actual twist of 8° x 360°, or 
2880°. But the bottom of the torsion thread was stiU 
twisted 12° as compared with the top, the force producing 
this twist corresponding to 12 x 35 (or 420°) of torsion; 
and to these the actual torsion of 12° must be added, 
making a total of 2880° -f- 420° + 12° = 3312. The 
result then of halving the distance between the magnet 
poles was to increase the force fourfold, for 3312 is very 
nearly four times 864. Had the distance between the 
poles been reduced to one-third the force would have been 
nine times as great. 

We may also, assuming this law proved, employ the 
balance to measure the strengths of magnet poles by 
measuring the forces they exert at known distances. 

133. Method of Oscillations.* — If a magnet sus- 
pended by a fine thread, or j)oised upon a point, be pushed 
aside from its position of rest, it will vibrate backwards 
and forwards, performing oscillations which, although 
they gradually decrease in amplitude, are executed in 



* It is possible, also, to measure electrical forces by a " method of os- 
cillations " ; a small charged ball at the end of a horizontally-suspended ai-m 
being caused to oscillate under the attracting force of a charged conductor 
near it, whose " force " at that distance is proportional to the square of the 
number of oscillations in a given time. 



122 ELECTRICITY AND MAGNETISM part i 

very nearly equal times. In fact, they follow a law similar 
fco that of the oscillations executed by a pendulum swing- 
ing under the influence of gravity. The law of pendular 
vibrations is, that the square of the number of oscillations 
executed in a given time is proportional to the force. Hence 
we can measure magnetic forces by counting the oscilla- 
tions made in a minute by a magnet. It must be 
remembered, however, that the actual number of oscilla- 
tions made by any given magnet will depend on the 
weight of the magnet and on its leverage around its 
centre, as well as upon the strength of its poles, and on 
the intensity of the field in which it may be placed (see 
calculations, Art. 361). 

We can use this method to compare the intensity of 
the force of the earth's magnetism * at any place with that 
at any other place on the earth's surface, by oscillating a 
magnet at one place and then taking it to the other place 
and oscillating it there. If, at the first, it makes a 
oscillations in one minute, and at the second h oscillations 
a minute, then the magnetic forces at the two places will 
be to one another in the ratio of a^ to h\ 

Again, we may use the method to compare the force 
exerted at any point by a magnet near it with the force 
of the earth's magnetism at that point. For, if we swing 
a small magnetic needle there, and find that it makes m 
oscillations a minute under the joint action f of the earth's 
magnetism, and that of the neighbouring magnet, and 
that, when the magnet is removed, it makes n oscillations 
a minute under the influence of the earth's magnetism 
alone, then m^ will be proportional to the joint forces, n^ 
to the force due to the earth's magnetism, and the differ- 
ence of these, or m^- n^ will be proportional to the force 
due to the neighbouring magnet. 

* Or, more strictly, of its horizontal component. 

t We are liere assuming that the magnet is so placed that its force is in 
a hne with that of the earth's magnetism at the point, and that the other 
pole of the magnet is so far away as not to aflfect the oscillating needle. 



:hap. II DISTRIBUTION ON SURFACE 



123 



:*•-■ 



6 — 
5— 
4.._- 

3 — 



134. Surface Distribution. — We will now apply the 
method of oscillations to measure the relative quantities 
of surface magnetism at different points along a bar 
magnet. The magnet to be examined is set up vertically 
(Fig. 79). A small magnet, capable of swinging hori- 
zontally, is brought near it and set at a short distance 
away from its extremity, and then oscillated, while the 
rate of its oscillations is counted. Suppose 
the needle were such that, when exposed 
to the earth's magnetism alone, it would 
perform 3 complete oscillations a minute, 
and that, when vibrating at its place near 
the end of the vertical magnet it oscillated 
14 times a minute, then the force due 
to the magnet will be proportional to 
1^2 _ 32 =, 196 _ 9 = 187. iS^extly, let 
the oscillating magnet be brought to an 
equal distance opposite a point a little 
away from the end of the vertical magnet. 
K, here, it oscillated 12 times a minute, 
we know that the force will be propor- 
tional to 122 _ 32 = 144 - 9 = 135. So 
we shall find that as the force falls off the oscillations 
will be fewer, until, when we put the oscillating magnet 
opposite the middle of the vertical magnet, we shall find 
that the number of oscillations is 3 per minute, or that 
the earth's force is the only force affecting the oscillations. 
In Fig. 80 we have indicated the number of oscillations 



S 

Fig. 79. 



at successive points, as 14, 12, 10, 8, 6, 5, 4, and 3. 
K we square these numbers and subtract 9 from each, 
we shall get for the forces at the various points the 
following : — 187, 135, 91, 55, 27, 16, 7, and 0. These 
forces may be taken to represent the strength of the free 
magnetism at the various points, and it is convenient to 
plot them out graphically in the manner shown in Fig. 80, 
where the heights of the dotted lines are chosen to a scale 
to represent proportionally the forces. The curve which 



124 ELECTKICITY AND MAGNETISM part i 

joins the tops of these ordinates shows graphically how 
the force, which is greatest at the end, falls off toward 
the middle. On a distant magnet pole these forces, thus 
represented by this curvilinear triangle, would act as if 



IN i I i "" T"--^—- s 

iMi!liK:i; I J :' . ' vii' -i ■■' - ^ II JMillllll | |||||| II i III |||||1|||| I IllillliPHIj 



i 

Fig. SO. 

concentrated at a point in the magnet opposite the " centre 
of gravity " of this triangle ; or, in other words, the " pole," 
which is the centre of the resultant forces, is not at the 
end of the magnet. In thin bars of magnetized steel it is 
at about Jj of the magnet's length from the end. 

135. Magnetic Moment. — It is found that the ten- 
dency of a magnet to turn or to be turned by another 
magnet depends not only on the strength jn.oi its poles, but 
the length I between them. The product of these two quan- 
tities m X Z is called the magnetic moment of the magnet, 
and is sometimes denoted by the symbol M. As the exact 
position of a magnet's poles is often unknown, it is easier 
to determine M than to measure either m or I separately. 

136. Method of Deflexions. — There are a number 
of ways in which the deflexion of a magnet by another 
magnet may be made use of to measure magnetic forces.* 

* The student desirous of mastering these methods of measuring mag- 
netic forces should consult Professor Andrew Gray's Absolute Measure- 
ments in Electricity and Magnetism. 



METHOD OF DEFLEXIONS 



125 



We cannot here give more than a glance at first prmciples. 
When two equal and opposite forces act on the ends of a 
rigid bar they simply tend to turn it round. Such a pair 
of forces form what is called a " couple," and the torque, 
or tendency to turn (formerly called the " moment " of the 
couple), is obtained by multiplying one of the two forces 
by the perpendicular distance between the directions of 
the forces. Such a couple tends to produce a motion of 
rotation, but not a motion of translation. Now a mag- 
netic needle placed in a 
magnetic field across the 
lines of force experiences 
a torque, tending to rotate 
it round into the magnetic 
meridian, for the X-seek- 
ing pole is urged north- 
wards, and the S-seeking 
pole is urged southwards, 
with an equal and opposite 
force. The force acting 
on each pole is the pro- 
duct of the strength of the 
pole and the intensity of 
the "field," that is to say, 
of the horizontal com- 
ponent of the force of the 
earth's magnetism at the 
place. We will call the 
strength of the ^-seeking pole m ; and we will use the 
symbol H to represent the force which the earth's 
magnetism would exert in a horizontal direction on 
a unit of magnetism. (The value of H is different 
at different regions of the globe.) The force on the 
pole A (see Fig. 81) will be then m x H, and that on 
pole B will be equal and opposite. We take NS as 
the direction of the magnetic meridian : the forces will 
be parallel to this direction. Now, the needle AB lies 



~W^' 




Fig. 81. 



126 ELECTEICITY AND MAGNETISM part i 

obliquely in the field, while the magnetic force acting on 
A is in the direction of the line PA, and that on B in 
the direction QB, as shown by the arrows. PQ is the 
perpendicular distance between these forces ; hence the 
"moment" of the couple, or torque, will be got by 
multiplying the length PQ by the force exerted on one 
of the poles. Usmg the symbol Y for the torque, we 
may write 

Y = PQ X m • H. 

But PQ is equal to the length of the magnet multiplied 
by the sine * of the angle AOR, which is the angle of 
deflexion, and which we will call S. Hence, using / for 
the length between the poles of the magnet, we may 
write the expression for the moment of the couple. 

Y = mm ■ sin 5. 

In words this is : the torque acting on the needle is 
proportional to its "magnetic moment" (m x /), to the 
horizontal force of the earth's magnetism, and to the sine 
of the angle of deflexion. 

The reader will not have failed to notice that if the 
needle were turned more obliquely, the distance PQ 
would be longer, and would be greatest if the needle 
were turned round east-and-west, or in the direction 
EW. Also the torque tending to rotate the magnet 
will be less and less as the needle is turned more nearly 
into the direction ISTS. 

137, Law of Tangents . — Now, let us suppose that the 
deflexion 8 were produced by a magnetic force applied at 
right angles to the jnagnetic meridian, and tending to draw 
the pole A in the direction RA. The length of the line RT 
multiplied by the new force will be the leverage of the 
new couple tending to twist the magnet into the direction 

* If any reader is unacquainted with trigonometrical terms he should 
consult the note at the end of this lesson, on " Ways of Eeckoning 
Angles." 



MAGNETOMETERS 



127 



EW. Xow. if the needle has come to rest in equilibrium 
between these Uxo forces, it is clear that the two opposing 
twists are just equal and oj^posite in power, or that the 
torque due to one couple is equal to that of the other 
couple. Hence the force in the dkection WE will be to 
the force in the direction SX in the same ratio as PQ is 
to RT, or as PO is to RO. 



Or, calling this force /, 

/: H = PO : RO. 



Or 



/=H: 




But PO = AR and |^ = tan 8, hence 
f =li tan 8 ; 

or, in other words, the magnetic force which, acting at right 
angles to the meridian, produces on a magnetic needle the 
deflexion 8, is equal to the horizontal force of the earth's 
magnetism at that point, multiplied hy the tangent of the 
angle of deflexion. Hence, also, 
two different magnetic forces act- 
ing at right angles to the meridian 
would severally deflect the needle 
through angles whose tangents are 
proportional to the forces. 

This very important theorem 
is applied in the construction of 
certain galvanometers (see Art. 
212). 

138. Magnetometers. — The 
name Magnetometer is given to 
any magnet specially arranged 
as an instrument for the purpose 
of measuring magnetic forces. 
The methods of observing the 
absolute values of magnetic forces in dyne-units (units 
in the " C.G.S." system) will be explained in Art. 361 



Fig. 82. 



Fie. S3. 



128 ELECTRICITY AND MAGNETISM part i 

at the end of Lesson XXVII. Very simple magneto- 
meters, consisting of small needles pivoted, or suspended 
by a fibre, are commonly used for measuring the relative 
values of magnetic forces. One very sensitive form (Fig. 
82), to be used, like the reflecting galvanometer (Art. 
215). with a beam of light as a pointer, consists of a smaU 

thin silvered glass mir- 
"^ ror, a half -inch or less 

-> in diameter, having 
two or three very light 
magnets cemented at 
its back, suspended by 
a single thread of cocoon silk, and enclosed in a suitable 
case. Another useful form (Fig. 83) consists of a short 
compass-needle poised on a pivot having a light index 
of aluminium long enough to move over a scale divided 
into tangent values (see Art. 212). 

A convenient deflexion magnetometer for comparing 
the magnetic moments (Art. 135) of two magnets is 

N 
First Positio7i. y^^^^^^ 



Fig. 84. 

afforded by such a tangent compass placed in the middle 
of a graduated platform (Fig. 84). There are two 
methods of using this apparatus. 

First Position : End-on Method. — The platform being 
set magnetically east and west, the deflecting mag-net is 
set end-on. Lender these circumstances the force is found 
to vary dii-ectly as the magnetic moment (Art. 135), and 
inversely as the cube of the distance between the centres of 
the magnets, or in symbols : — 

/ = 2^1 r3. 



^[AGNETOMETRIC METHODS 



129 



But we have seen above that where magnetic force is 
measured by a deflexion 8 at a place where the H is 
earth's horizontal magnetic force, / is equal to H tan B ; 
so that 

2M/r3 = H tan 8, 
whence 

M = ir3H tan 8. 



Second Position : Broadside-on. — The platform being 
turned into the north-south position, the deflecting 
magnet is set broadside-on. In this 
case the magnet deflects the needle in 
the other dii-ection and with half the 
force that it would have exerted at an 
equal distance in the end-on position. 
But the force still varies inversely as 
the cube of the distance : the formula 
being now 

whence 

M = rm tan 8. 

139. Balance Methods. — In 

either position of the magnetometer 
platform two magnets can be placed 
on the two sides of the board so as to 
balance one another's effects by adjust- 
ing them to proper distances. This 
gives a comparison of their magnetic 
moments in terms of their respective 
distances, or 

M^ : M2 = r^3 . r^3^ 

140. Hughes's Magnetic Balance. 
— A very convenient instrument for testing the mag- 
netic properties of different specimens of iron and steel 
was devised by Hughes in 1884. The sample to be tested 




130 



ELECTEICITY AND MAGNETISM 



is placed in a magnetizing coil A (Fig. 86), and a current 
is sent round it. It deflects a lightly-suspended indicating 
needle B, which is then brought to zero by turning a 
large compensating magnet M upon its centre. A small 
coil C is added to balance the direct deflecting effect due 




Fig. 86. 

to coil A. The author of this book has shown that if the 
distance from M to B is 2-3 times the length of M, the 
angle through which M is turned is proportional to 
the magnetic force due to the iron core at A, provided 
the angle is less than 60°. 

141. Unit Strength of Pole. — The Second Law of 
Magnetic Force (see Art. 128) stated that the force exerted 
between two poles was proportional to the product of 
their strengths, and was inversely proportional to the 
square of the distance between them. It is possible to 
choose such a strength of pole that this proportionality 
shall become numerically an equality. In order that this 
may be so, we must adopt the following as our unit of 
strength of a pole, or unit magnetic pole : A Unit Mag- 
netic Pole is one of such a strength that, when placed at a 
distance of one centimetre from a siynilar pole of equal 
strength it repels it ivith a force of one dyne (see Art. 352). 
If we adopt this definition we may express the second 
law of magnetic force in the following equation : — 



/ 



d2 



CHAP. II THEORY OF MAGNETIC CURVES 131 

where /is the force (in dynes), 7n and 7n' the strengths of 
the two poles, and d the distance between them (in centi- 
metres). From this definition is derived tlie arbitrary- 
convention about magnetic lines. If at any place in a 
magnetic field we imagine a unit magnetic pole to be set 
it will be acted upon, tending to move along the lines of 
the field. Then if at that place we find the force on the 
pole to be H djmes, w^e may conceive that there are H 
lines drawn per square centimetre. For example, if we 
describe the field as having 50 lines side by side per 
square centimetre, we mean that a unit pole placed there 
WT.11 be acted on with a force of 50 dynes. This subject 
is resumed in Lesson XXYL, Art. 338, on the Theory of 
Magnetic Potential. 

142. Theory of Magnetic Curves. — We saw (Art. 
119) that magnetic figures are produced by iron filings 
setting themselves in certain directions in the field of 
force around a magnet. We can now apply the law of 
inverse squares to aid us in determining the direction 
in which a filing will set itself at any point in the 
field. Let NS (Fig. 87) be a long thin magnet, and P 
any point in the field due to its magnetism. If the N- 
seeking pole of a small magnet be put at P, it will be 
attracted by S and repelled by N ; the directions of these 
two forces will be along the lines PS and PN. The 
amounts of the forces may be represented by certain 
lengths marked out along these lines. Suppose the dis- 
tance PX is twice as great as PS, the repelling force along 
PIST will be ^ as strong as the attracting force along PS. 
So measure a distance out, PA towards S four times as 
long as the length PB measured along PN away from 
N. Find the resultant force in the usual way of com- 
pounding mechanical forces, by completing the parallelo- 
gram PARE ; the diagonal PR represents by its length 
and direction the magnitude and the direction of the 
resultant magnetic force at the point P. In fact the line 
PR represents the line along which a small magnet or an 



132 ELECTEICITY AND MAGNETISM part i 

iron filing would set itself. In a similar way we might 
ascertain the direction of the lines of force at any point 
of the field. The little arrows in Fig. 87 show how the 
lines of force start out from the X pole and curve round 
to meet in the S pole. The student should compare this 




/ 




llfallllllllllllllllllllllllllllllllllllllllllllllllll^ 



/ 



'i^ 



Fig. ST. 



figure with the lines of filings of Fig. 67. Henceforth we 
must think of every magnet as being permeated by these 
magnetic lines which extend out into the surrounding 
space. The whole number of magnetic lines which run 
through a magnet is termed its magnetic flux (Art. 337). 

143- A Magnetic Paradox. — If the X-seeking pole 
of a strong magnet be held at some distance from the 
X-seeking pole of a weak magnet, it will repel it ; but 
if it is pushed up quite close it will be found now to 
attract it. This paradoxical experiment is explained by 
the fact that the magnetism induced in the weak mag- 
net by the powerful one will be of the opposite kind, 
and will be attracted ; and, when the powerful magnet 
is near, this induced magnetism may overpower and 
mask the original magnetism of the weak magnet. The 



CHAP. II RECKONING OF ANGLES 133 

student must be cautioned that in most of the experi- 
ments on magnet poles similar perturbing causes are at 
work. The magnetism in a magnet is not quite fixed, 
but is liable to be disturbed in its distribution by the 
near presence of other magnet poles, for no steel is so 
hard as not to be temporarily affected by magnetic 
induction. 

XoTE ON Ways of Keckoning Angles and Solid 
Angles 

144. Reckoning in Degrees. — When two straight lines cross 
one another they form an foi.^/e between them; and tliis angle 
may be defined as the amount of rotation which one of the lines 
has performed round a fixed point in 
the other line. Thus we may suppose 
the line CP in Fig. 88 to have originally 
lain along CO, and then turned round 
to its present position. The amount by 
which it has been rotated is clearly a cer- 
tain fraction of the whole way round ; 
and the amount of rotation round C we 
call " the angle which PC makes with 
OC," or more simply " the angle PCO." 
But there are a number of different 
ways of reckoning this angle. The 
common way is to reckon the angle by 
" degrees " of arc. Thus, suppose a circle to be drawn round C, 
if the circumference of the circle were divided into 360 parts 
each part would be called " one degree " (1°), and the angle 
would be reckoned by naming the number of such degrees along 

the curved arc OP. In the figure the arc is about 571°, or - '* 
^ '360 

of the whole way round, no matter what size the circle is drawn. 

145. Reckoning in Radians. — A more sensible but less usual 
way to express an angle is to reckon it by the ratio between the 
length of the curved arc that "subtends" the angle and the 
length of the radius of the circle. Suppose we have drawn round 
the centre C a circle whose radius is one centimetre, the diam- 
eter will be tivo centimetres. The length of the circumference 
all round is known to be about 3r times the lengtli of the diam- 
eter, or more exactly 3" 14159. . . . This number is so awkward 




134 



ELECTRICITY AND MAGNETISM part i 



that, for convenience, vre always use for it the Greek letter n. 
Hence the length of the circumference of our circle, whose radius 
is one centimetre, will be 6'2831S . . . centimetres, or 27r centi- 
metres. We can then reckon any angle by naming the length of 
arc that subtends it on a circle one centimetre in radius. If we 
choose the angle PCO, such that the curved arc OP shall be just 
one centimetre long, this will be the angle one, or unit of angular 
measure, or, as it is sometimes called, the angle PCO will be one 

360^ 
" radian." In degree-measure one radian = — — - = 57° 17' nearly. 

All the way round the circle will be 27r radians. A right angle 
will be ^ radians. 

146. Reckoning by Sines or Cosines. — In trigonometry 

other ways of reckoning angles are used, in which, however, the 
angles themselves are not reckoned, but 
certain "functions " of them called "sines," 
"cosines," "tangents," etc. For readers 
not accustomed to these we will briefly 
explain the geometrical nature of these 
"functions." Suppose we draw (Fig. 89) 
our circle as before round centre C, and 
then drop down a i5lumb-line PM, on to the 
line CO ; we will, instead of reckoning the 
angle by the curved arc, reckon it by the 
length of the line PM. It is clear that 

if the angle is small, PM will be short ; but as the angle opens 

out towards a right angle, PM will get longer and longer (Fig. 

90) . The ratio between the length of this line and the radius 

of the circle is called the "sine" of the 

angle, and if the radius is 1 the length of 

PM will be the value of the sine. It can 

never be greater than 1, though it may 

have all values between 1 and — 1. The 

length of the line CM will also depend upon 

the amount of the angle. If the angle is 

small CM will be nearly as long as CO; 

if the angle open out to nearly a right angle 

CM wiU be very short. The length of CM (when the radius is 1) 

is called the " cosine " of the angle. If the angle be called 6, then 

we may for shortness write these functions : 

PM 
CP 
CM 
CP" 





Sin 



Cos a 



SOLID ANGLES 



135 



147. Reckoning by Tangents. — Siippose we draw our circle 
as before (Fig. 91) , but at the point O draw a straight line touch- 
ing the circle, the tangent line at O ; let us 

also prolong CP until it meets the tangent 

line at T. We may measure the angle 

between OC and OP in terms of the length 

of the tangent OT as compared with the 

length of the radius. Since our radius is 

1, this ratio is numerically the length of 

OT, and we may therefore call the length 

of OT the " tangent " of the angle OCR 

It is clear that smaller angles will have / 

smaller tangents, but that larger angles i 

may have very large tangents ; in fact, \ 

the length of the tangent when PC was 

moved round to a right angle would be 

infinitely great. It can be shown that the 

ratio between the lengths of the sine and 

of the cosine of the angle is the same as 

the ratio between the length of the tangent and that of the 

radius ; or the tangent of an angle is equal to its sine divided 

by its cosine. The formula for the tangent may be written: 

TO ^ PM. 

OC MC" 

148, Solid Aug-les. — When three or more surfaces inter- 
sect at a point they form a solid angle : there is a solid angle, 

for example, at the top of a 




Fig-. 91. 



tan 



pyramid, or of a cone, and one 
at every corner of a diamond 
that has been cut. If a surface 
of any given shape be near a 
point, it is said to subtend a 
certain solid angle at that 
point, the solid angle being- 
mapped out by drawing lines 
from all points of the edge of 
this surface to the point P (Fig. 
92). An irregular cone will 
thus be generated whose solid 
angle is the solid angle sub- 
tended at P by the surface EF. To reckon this solid angle we 
adopt an expedient similar to that adopted when we wished 
to reckon a plane angle in radians. About the point P, with 
radius of 1 centimetre, describe a sphere^ which will intercept 




Fi":. 92. 



136 



ELECTRICITY AND MAGXETISM part i 



the cone over an area INIX : the area thus intercepted measures 
the soM angle. If the sphere have the radius 1, its total surface 
is 4:77. The solid angle subtended at the centre by a hemisphere 
would be 2-. It -vrill be seen that the ratio between the area of 
the surface EF and the area of the surface ^IX is the ratio 
between the squares of the lines EP and MP. The solid angle 
subtended br a surface at a point (other things being equal) is 
inversely proportional to the square of its distance from the 
point. This is the basis of the law of inverse squares. 

A table of radians, sines, tangents, etc., is given at the end 
of this book as Appendix A. 



Lessox XII. — Terrestrial Magnetism 

149. The Mariner's Compass. — It was mentioned 
in Art. ST that the compass sold by opticians consists of 




a magnetized steel needle balanced on a fine point above 
a card marked out X, S, E, AV, etc. The Mariner's 
Compass is, however, somewhat differently arranged. 
In Fig. 93 one of the forms of a Mariner's Compass, 



CHAP. II TERRESTRIAL MAGNETISM 137 

used for nautical observations, is shown. Here the card, 
divided out into the 32 '' points of the compass," is itself 
attached to the needle, and swings round with it so that 
the point marked X on the card always points to the 
north. In the best modern ships' compasses, such as 
those of Lord Kelvin, several magnetized needles are 
placed side by side, as it is fomid that the indications of 
such a compound needle are more reliable. The iron 
fittings of wooden vessels, and, in the case of iron vessels, 
the ships themselves, affect the compass, which has there- 
fore to be corrected by placing conjpensating masses of 
iron near it, or by fixing it high upon a mast. The 
error of the compass due to magnetism of the ship is 
known as the deviation. 

150. The Earth a Magnet. — Gilbert made the great 
discovery that the compass-needle points north and south 
because the earth is itself also a great magnet. The 
magnetic poles of the earth are, however, not exactly at 
the geographical north and south poles. The magnetic 
north pole of the earth is more than 1000 miles away 
from the actual pole, being in lat. 70° 5' IST., and long. 
96° 46' W. In 1831, it was found by Sir J. C. Ross to 
be situated in Boothia Felix, just within the Arctic 
Ch'cle. The south magnetic pole of the earth has never 
been reached ; and by reason of irregularities in the 
distribution of the magnetism there appear to be two 
south magnetic polar regions. 

151. Declination. — In consequence of this natural 
distribution the compass-needle does not at all points of 
the earth's surface point truly north and south. Thus, in 
1894, the compass-needle at London pointed at an angle 
of about 17° west of the true north ; in 1900 it will be 
16° 16'. This angle between the magnetic meridian * and 

* The Magnetic Meridian of any place is an imag-inary plane drawn 
through the zenith, and passing through the magnetic north point and 
magnetic south point of the horizon, as observed at that place by the 
pointing of a horizontally-suspended compass-needle. 



138 



ELECTRICITY AND MAGNETISM part i 



the geographical meridian of a place is called the magnetic 
Declination of that place. The existence of this declina- 
tion was discovered by Columbus in 1492, though it 
appears to have been previously known to the Chinese, 
and is said to have been noticed in Europe in the early 
part of the thirteenth century by Peter Peregrinus. The 
fact that the declination differs at different points of the 
earth's surface, is the undisputed discovery of Columbus. 
In order that ships may steer by the compass, magnetic 
charts (Art. 154) must be prepared, and the declination at 
different places accurately measured. The upright pieces 
P, P', on the " azimuth compass " drawn in Fig. 93, are 
for the purpose of sighting a star whose position may 
be known from astronomical tables, and thus affording 

a comparison be- 
tween the magnetic 
meridian of the 
place and the geo- 
graphical meridian, 
and of measuring 
the angle between 
them. 

152. Inclina- 
tion or Dip. — Nor- 
man, an instru- 
ment - maker, dis- 
covered in 1576 
that a balanced 
needle, when mag- 
netized, tends to 
dip downwards to- 
ward the north. 
He therefore con- 
structed a Dip- 
ping-Needle, capa- 
ble of turning in a vertical plane about a horizontal axis, 
with which he found the " dip " to be (at London) an 




Fig. ai. 



MAGNETIC DIP 



139 



angle of 71° 50'. A simple form of dipping-needle is 
shown in Fig. 94. The dip-circles used in the ma-gnetic 
observatory at Kew are much more exact and delicate 
instruments. It was, however, found that the dip, like 
the declination, differs at different parts of the earth's 
surface, and that it also undergoes changes from year to 
year. The " dip " in London for the year 1894 is 67° 18' ; 
in 1900 it will be 67° 9'. At the north magnetic pole 
the needle dips straight down. The following table 
gives particulars of the Declination, Inclination, and 
total magnetic force at a number of important places, 
the values being approximately true for the year 1900. 

Table of Magnetic Declination and Inclination 
(for Year 1900) 



Localitj-. 


Declination. 


Dip. 


Total Force 
(C.G.S.). 


London . . . 
St. Petersburg 
Berlin .... 

Paris 

Rome .... 
iSTew York . . 
Washington . 
San Francisco 
Mexico .... 




16° 16' W. 

0° 30' E. 

9° 30' W. 
14° 30' W. 
10° 0' W. 

9° 12' W. 

4° 35' W. 
16° 42' E. 

8°0' E. 
25° 0' W. 
29° 24' W. 

9° 36' E. 
25° 0' E. 

0° 36' E. 

4° 6' W. 


67° 9' N. 
70° 46' N. 
66° 43' N. 
64° 55' N. 
58° 0' N. 
70° C' N. 
70° 18' N. 
62° 20' N. 
45° 1' N. 
32° 12' S. 
58° 2' S. 
62° 45' S. 
71° 12' S. 
20° 38' N. 
49° 52' N. 


0-47 
0-48 
0-48 
0-47 
0-45 
0-61 
0-60 
0-54 
0-48 
0-31 
0-36 
0-57 
0-64 
0-37 
0-45 


St. Helena . . 
Cape Town . 
Sydney . . . 
Hobarton . . 
Bombay . . . 
Tokio .... 



153. Intensity. — Three things must be known in 
order to specify exactly the magnetism at any place ; 
these three elements are : 



140 ELECTRICITY AND MAGNETISM part i 

The Declination ; 

The Inclination, and 

The Intensity of the Magnetic Force. 

The magnetic force is measured by one of the methods 
mentioned in the preceding lesson. Its direction is in 
the line of the dipping-needle, which, like every magnet, 
tends to set itself along the lines of force. It is, however, 
more convenient to measure the force not in its total 
intensity in the line of the dip, but to measure the 
horizontal component of the force, — that is to say, the 
force in the direction of the horizontal compass-needle, 
from which the total force can be calculated if the dip is 
known .* Or if the horizontal and vertical components of 
the force are known, the total force and the angle of the 
dip can both be calculated.! The horizontal component 
of the force, or " horizontal intensity," can be ascertained 
either by the method of Vibrations or by the method of 
Deflexions. The mean horizontal force of the earth's 
magnetism at London in 1890 was -1823 dyne-units, the 
mean vertical force 4377, the total force (in the line of dip) 
was 4741 dyne-units. The distribution of the magnetic 
force at different points of the earth's surface is irregular, 
and varies in different latitudes according to an approxi- 
mate law, which, as given by Biot, is that the force is pro- 
portional to Vl -f 3 sin^/, where / is the magnetic latitude. 

154. Magnetic Maps. — For purposes of convenience 
it is usual to construct magnetic maps, on which such 
data as these given in the Table on p. 139 can be marked 
down. Such maps may be constructed in several ways. 
Thus, it would be possible to take a map of England, or 
of the world, and mark it over with lines such as to 
represent by their direction the actual direction in which 
the compass points ; in fact to draw the lines of force or 

* For if H = Horizontal Component of Force, and I = Total Force, and 
6 = angle of dip, I = H ■=- cos 0. 

t For H2 + V2 = 12, where V = Vertical Component of Force. 



CHAP. II MAGNETIC MAPS 141 

magnetic meridians. A more useful way of marking the 
map is to find out those places at which the declination 
is the same, and to join these places by a line. The 
Magnetic Map of Great Britain, which forms the Frontis- 
piece to these lessons, is constructed on this plan from the 
magnetic survey lately made by Rucker and Thorpe . At 
Plymouth the compass-needle in 1900 will point 18° to 
the w^est of the geographical north. The declination at 
Lynton, at Shrewsbury, and at Berwick will in that year 
be the same as at Plymouth. Hence a line joining these 
towns may be called a line of equal declination, or an 
Isogonic line. It will be seen from this map that the 
declination is greater in the north-west of England than 
in the south-east. We might similarly construct a mag- 
netic map, marking itwdth lines joining places where the 
dip w'as equal ; such lines would be called Isoclinic lines. 
In England they run across the map from west-south-west 
to east-north-east. For example, in 1900 the needle will 
dip about 67° at London, Southampton, and Plymouth. 
Through these places then the isoclinic of 67° may be 
drawai for that epoch. On the globe the isogonic lines 
run for the most part from the north magnetic pole to the 
south magnetic polar region, but, owing to the irregulari- 
ties of distribution of the earth's magnetism, their forms 
are not simple. The isoclinic lines of the globe run round 
the earth like the parallels of latitude, but are irregular 
in form. Thus the line joining places where the north- 
seeking pole of the needle dips down 70° runs across 
England and Wales, passes the south of Ireland, then 
crosses the Atlantic in a south-westerly direction, traverses 
the United States, swerving northwards, and just crosses 
the southern tip of Alaska. It drops somewhat southward 
again as it crosses China, but again curves northwards as 
it enters Russian territory. Finally it crosses the south- 
ern part of the Baltic, and reaches England across the 
German Ocean. The magnetic chart of the United 
States, which is also given at the front of this book, is for 



142 ELECTRICITY AND MAGNETISM part i 

the year 1900. It has been prepared from data furnished 
"by Professor Mendenhall of the U.S. Geodetic Survey. 
It will be noticed that in the year 1900 the magnetic 
declination will be zero at Lansing (Mich.), Columbus 
(Ohio), and Charleston (S. Carolina). 

The line passing through places of no declination is 
called the agonic line. It passes across both hemispheres, 
crossing Eussia, Persia, and Australia. There is another 
agonic line in eastern Asia enclosing a region around 
Japan, within which there is a westerly declination. 

155. Variations of Earth's Magnetism. — We have 
already mentioned that both the declination and the 
inclination are subject to changes ; some of these changes 
take place very slowly, others occur every year, and others 
again every day. 

Those changes which require many years to run theu' 
course are called secular changes. 

The variations of the declination previous to 1580 are 
not recorded ; the compass at London then pointed 11° 
east of true north. This easterly declination gradually 
decreased, until in 1657 the compass pointed true north. 
It then moved westward, attaining a maximum of 24° 27' 
about the year 1816, from which time it has slowly dimin- 
ished to its present value (16° 57' in 1891) ; it diminishes 
(in England) at about the rate of 7' per year. At about 
the year 1976 it will again point truly north, making a 
complete cycle of changes in about 320 years. 

The Inclination in 1576 was 71° 50', and it slowly 
increased till 1720, when the angle of dip reached the 
maximum value of 74° 12'. It has since steadily dimin- 
ished to its present (1894) value of 67° 39'. The period 
in which the cycle is completed is not known, but the rate 
of variation of the dip is less at the present time than it 
was fifty years ago. In all parts of the earth both 
declination and inclination are slowly changing. The 
following table gives the data of the secular changes at 
London. 



MAGNETIC VARIATION 



143 



Table of Secular Magnetic Variations 



Year. 


Declination. 


Inclination. 


1576 




71° 50' 


1580 


11° 17' E. 




1600 




72° 0' 


1622 


6° 12' 




1634 


4°0' 




1657 


0° 0' min. 




1676 


3° 0' W. 


73° 30' 


1705 


9°0' 




1720 


13° 0' 


74° 42' max. 


1760 


19° 30' 




1780 




72° 8' 


1800 


24° 6' 


70° 35' 


1816 


24° 30' max. 




1830 


24° 2' 


69° 3' 


1855 


23° 0' 




1868 


20° 33' 


68° 2' 


1878 


19° 14' 


67° 43' 


1880 


18° 40' 


67° 40' 


1890 


17° 26' 


67° 23' 


1900 • 


16° 16' 


67° 9' 



The Total Magnetic force, or " Intensity," also slowly 
changes in value. As measured near London, it was 
equal to -4791 dyne-units in 1848, -4740 in 1866, in 
1880 -4736 dyne-units, in 1890 4741.* Owing to the 
steady decrease of the angle at which the needle dips, 
the horizontal component of this force (i.e. the " Hori- 
zontal Intensity") is slightly increasing. It was -1716 
dyne-units in 1814, -1797 dyne-units at the beginning of 
1880, and -1823 dyne-units in 1890. 

156. Daily Variations. — Both compass and dipping- 
needle, if minutely observed, exhibit slight daily mo- 

* That is to say, a north magnet pole of unit strength is urged in the 
hne of dip, with a mechanical force of a little less than half a dyne. 



144 ELECTRICITY AND MAGNETISM part i 

tions. About 7 a.m. the compass-needle begins to travel 
westward with a motion which lasts till about 1 p.m. ; 
during the afternoon and evening the needle slowly 
travels back eastward, until about 10 p.m. ; after this 
it rests quiet ; but in summer-time the needle begins 
to move again slightly to the west at about midnight, 
and returns again eastward before 7 a.m. These delicate 
variations — never more than 10' of arc — appear to 
be connected with the position of the sun ; and the moon 
also exercises a minute influence upon the position of 
the needle. 

157. Annual Variations. — There is also an annual 
variation corresponding with the movement of the earth 
around the sun. In the British Islands the total force 
is greatest in June and least in February, but in the 
Southern Hemisphere, in Tasmania, the reverse is the 
case. The dip also differs with the season of the year, 
the angle of dip being (in England) less during the f our 
summer months than in the rest of the year. 

158. Eleven -Year Period. — General Sabine dis- 
covered that there is a larger amount of variation of 
the declination occurring about once every eleven years. 
Schwabe noticed that the recm'rence of these periods 
coincided with the eleven-year periods at which there 
is a maximum of spots on the sun. Professor Balfour 
Stewart and others have endeavoured to trace a similar 
periodicity in the recurrence of aurorae * and of other 
phenomena. 

159. Magnetic Storms. — It is sometimes observed 
that a sudden (though very minute) u'regular disturbance 
will affect the whole of the compass-needles over a con- 
siderable region of the globe. Such occurrences are 
known as magnetic storms ; they frequently occur at the 
time when an aurora is visible. 

160. Self-recording Magnetic Apparatus. — At Kew 
and other magnetic observatories the daily and hourly 

* See Lesson XXIV., on Atmospheric Electricity. 



CHAP. II TERRESTRIAL MAGNETISM 145 

variations of the magnet are recorded on a continuous 
register. The means employed consists in throwing a 
beam of light from a lamp on to a light mirror attached 
to the magnet whose motion is to be observed. A spot 
of light is thus reflected upon a ribbon of photographic 
paper prepared so as to be sensitive to light. The paper 
is moved continuously forward by a clockwork train ; 
and if the magnet be at rest the dark trace on the paper 
will be simply a straight line. If, however, the magnet 
moves aside, the spot of light reflected from the mirror 
will be displaced, and the photographed line will be 
curved or crooked. Comparison of such records, or 
magnetograpTis, from stations widely apart on the earth's 
surface, promises to afford much light upon the cause of 
the changes of the earth's magnetism, to which hitherto 
no reliable origin has been with certainty assigned. 
Schuster has shown that these changes generally come 
from without, and not from within. 

161. Theory of Earth's Magnetism. — The phenome- 
non of earth-currents (Art. 233) appears to be con- 
nected with that of the changes in the earth's magnet- 
ism, and can be observed whenever there is a display of 
aurora, and during a magnetic storm ; but it is not yet 
determined whether these currents are due to the varia- 
tions in the magnetism of the earth, or whether these 
variations are due to the currents. It is known that the 
evaporation (see Art. 71) always going on in the tropics 
causes the ascending currents of heated air to be electri- 
fied positively relatively to the earth. These air-currents 
travel northward and southward toward the colder polar 
regions, where they descend. These streams of electri- 
fied air will act (see Art. 397) like true electric currents, 
and as the earth rotates within them it will be acted 
upon magnetically. The author has for twelve years 
upheld the view that this thermodynamic production 
of polar currents in conjunction with the earth's diurnal 
rotation affords the only rational means yet suggested 

L 



146 ELECTRICITY AND MAGNETISM pakt i 

for accounting for the growth of the earth's magnetism 
to its present state. The action of the sun and moon 
in raising tides in the atmosphere might account for the 
variations mentioned in Art. 155. It is important to 
note that in all magnetic storms the intensity of the 
perturbations is greatest in the regions nearest the poles ; 
also, that the magnetic poles coincide very nearly with 
the regions of greatest cold; that the region where 
aurorse (Art. 336) are seen in gTeatest abundance is a 
region lying nearly symmetrically round the magnetic 
pole. It may be added that the general dii-ection of the 
feeble daily earth-currents (Art. 233) is from the poles 
toward the equator. 



CHAPTER III 



CURRENT ELECTRICITY 

Lesson XIII. — Simple Voltaic Cells 

162. Flow of Currents. — It has been already men- 
tioned, in Lesson lY., how electricity flows away from 
a charged body through any conducting substance, such 
as a wire or a wetted string. If, by any arrangement, 
electricity could be supplied to the body just as fast as 
it flowed away, a continuous current would be produced. 
Such a current always flows through a conducting wire, 
if the ends are kept at different electric potentials. In 
like manner, a current of heat flows through a rod of 
metal if the ends are kept at different temperatures, the 
flow being alM'^ays from the high temperature to the 
lower. No exact evidence exists as to the direction in 
which the current in a wire really "flows." It is con- 
venient to regard the electricity as flowing from positive 
to negative ; or, in other words, the natural direction 
of an electric current is from the high potential to the 
low. It is obvious that such a flow tends to bring both 
to one level of potential. In order that a continuous 
flow may be kept up there must be a circuit provided. 
The " current " has sometimes been regarded as a double 
transfer of positive electricity in one direction, and of 
negative electricity in the opposite direction. The only 
evidence to support this very unnecessary supposition 
147 



148 ELECTEICITY AND MAGNETISM. part i 

is the fact that, in the decomposition of liquids by the 
current, some of the elements are liberated at the place 
where the current enters, others at the place where it 
leaves the liquid. 

The quantity of electricity conveyed by a current is 
proportional to the current and to the time that it con- 
tinues to flow. The practical unit of current is called the 
ampere (see Arts. 207 and 254). The quantity of electri- 
city conveyed by a current of one arnpere in one second is 
called one ampere-second or one coulomb. One ampere- 
Jwur equals 3600 coxdomhs. If C is the number of 
amperes of cm-rent, t the number of seconds that it lasts, 
and Q, the number of coulombs of electricity thereby con- 
veyed, the relation between them is expressed by the 
formula : — 

Q = C X ^ 

Example. — If a current of 80 amperes flows for 15 minutes 
the total quantity of electricity conveyed will be 
80 X 15 X 60 = 72,000 coulombs. This is equal to 20 
ampere-hours. 

Currents are called continuous if they flow, without 
stopping, in one direction. They are called alternate 
currents if they continually reverse in direction in a 
regular periodic manner, flowing first in one direction 
round the circuit and then in the other. 

Continuous currents of electricity, such as we have 
described, are produced by voltaic cells, and batteries of 
such cells, or else by dynamos driven by power, though 
there are other sources of currents hereafter to be men- 
tioned. Alternate currents are produced by special 
alternate current dynamos or alternators, and are sepa- 
rately treated of in Art. 470. 

163. Discoveries of Galvani and of Volta. — The dis- 
covery of electric currents originated with Galvayii, a 
physician of Bologna, who, about the year 1786, made a 
series of ciuious and important observations upon the 



CHAP. Ill 



THE VOLTAIC PILE 



149 



convulsiye motions produced by the "return-shock" (Art. 
29) and other electric discharges upon a frog's leg. He 
was led by this to the discovery that it was not necessary 
to use an electric machine to produce these effects, but 
that a similar convulsive kick was produced in the frog's 
leg when two dissimilar metals, iron and copper, for 
example, were placed in contact with a nerve and a 
muscle respectively, and then brought into contact with 
each other. Galvani imagined this action to be due to 
electricity generated by the frog's leg itself. It was, 
however, proved by Volta, Professor in the University 
of Pavia, that the electricity arose not from the muscle 
or nerve, but from the contact of the dissimilar metals. 
When two metals are -placed in contact with one another 
in the air, one becomes positive and the other negative, 
as we have seen near the end of Lesson VII., though the 
charges are very feeble. Volta, however, proved their 
reality by two different methods. 

164. The Voltaic Pile. — The second of Volta's 
proofs was less direct, but even more convincing; and 
consisted in showing that when a num- 
ber of such contacts of dissimilar metals 
could be arranged so as to add their 
electrical effects together, those effects 
were more powerful in proportion to the 
number of the contacts. With this view 
he constructed the apparatus known (in 
honour of the discoverer) as the Voltaic 
Pile (Fig. 95). It is made by placing a 
pair of disks of zinc and copper in contact 
with one another, then laying on the 
copper disk a piece of flannel or blotting- 
paper moistened with brine, then another 
pair of disks of zinc and copper, and so 
on, each pair of disks in the pile being 
separated by a moist conductor. Such a pile, if composed 
of a number of such pairs of disks, will produce electricity 




Fiff. 95. 



150 



ELECTRICITY AND MAGNETISM part i 



enough to give quite a perceptible shock, if the top and 
bottom disks, or wires connected with them, be touched 
simultaneously with the moist fingers. When a single 
pair of metals are placed in contact, one becomes + ly 
electrical to a certain small extent, and the other — ly 
electrical, or, in other words, there is a certain difference of 
electric potential (see Art. 265) between them. But when 
a number are thus set in series with moist conductors 
between the successive pau's, the difference of potential 
between the first zinc and the last copper disk is increased 
in proportion to the number of pairs; for now all the 
successive small differences of potential are added together. 
165. The Crown of Cups. — Another combination 
devised by Yolta was his Couronne de Tasses or Crown 
of Cups. It consisted of a number of cups (Fig. 96), 
filled either with brine or dilute acid, into which dipped 
a number of compound strips, liaK zinc, half copper, 
the zinc portion of one strip dipping into one cup, while 




Fig. m. 



the copper portion dipped into the other cup. The 
difference of potential between the first and last cups 
is again proportional to the number of pairs of metal 
strips. This arrangement, though badly adapted for 
such a purpose, is powerful enough to ring an electric 
bell, the wires of which are joined to the first zinc and 
the last copper strip. The electrical action of these 



CHAP. Ill 



VOLTAIC CELL 



151 



combinations is, however, best understood by studying 
the phenomena of one single cup or cell. 

166. Simple Voltaic Cell. — Place in a glass jar 
some water having a little sulphuric acid or any other 
oxidizing acid added to it (Fig. 97). Place in it sep- 
arately two clean strips, one of zinc Z, and one of copper 
C. This cell is 
capable of supply- 
ing a continuous 
flow of electricity 
through a wire 
whose ends are 
brought into con- 
nexion with the 
two strips. When 
the current flows 
the zinc strip is 
observed to waste 
away ; its consump- 
tion in fact fur- 
nishes the energy 
required to drive 
the current through 
the cell and the 
connecting wire. 
The cell may therefore be regarded as a sort of chemical 
furnace in which fuel is consumed to drive the current. 
The zinc is the fuel,* the acid is the aliment, whilst the 
copper is merely a metallic hand let down into the cell 
to pick up the current, and takes no part chemically. 
Before the strips are connected by a wire no appreciable 
difference of potential between the copper and the zinc 
will be observed by an electrometer ; because the electro- 
meter only measures the potential at a point in the air or 
oxidizing medium outside the zinc or the copper, not the 

* Zinc, as is well known, will burn ^vith r, blue flame iu air or oxygen, 
giving out heat. Zinc foU is easily kindled. 




Fig. 97. 



152 ELECTRICITY AND MAGNETISM part i 

potentials of the metals themselves. The zinc is trying 
to dissolve and throw a current across to the copper ; 
while the copper is trying (less powerfully) to dissolve 
and throw a current across the other way. The zinc 
itself is at about 1-86 volts higher potential than the 
surrounding oxidizing media (see Art. 489) ; while the 
copper is at only about -81 volts higher, having a less 
tendency to become oxidized. There is then a latent 
difference of potential of about 1-05 volts between the 
zinc and the copper ; but this produces no current as 
long as there is no metallic circuit. If the strips are 
made to touch, or are joined by a pair of metal wires, 
immediately there is a rush of electricity through the acid 
from the zinc to the copper, as indicated by the arrows 
in Fig. 97, the current returning by the metal circuit 
from the copper to the zinc. A small portion of the zinc 
is at the same time dissolved away ; the zinc parting 
with its latent energy as its atoms combine with the acid. 
This energy is expended in forcing electricity through 
the acid to the coj^per strip, and thence through the wire 
circuit back to the zinc strip. The copper strip, whence 
the current starts on its journej^ through the external 
circuit, is called the positive pole, and the zinc strip is 
called the negative pole. If two copper wires are united 
to the tops of the two strips, though no current flows so 
long as the wires are kept separate, the wire attached to 
the zinc will be found to be negative, and that attached 
to the copper positive, there being still a tendency for 
the zinc to oxidize and drive electricity through the cell 
from zinc to copper. This state of things is represented 
by the + and — signs in Fig. 97; and this distribution 
of potentials led some to consider the junction of the zinc 
with the copper wire as the starting point of the current. 
But the real starting point is in the cell at the surface of 
the zinc where the chemical action is furnishing energy; 
for from this point there are propagated through the 
liquid certain electro-chemical actions (more fully ex- 



CHAP. Ill BATTERIES OF CELLS 153 

plained iii Chap. XI.) which have the result of constantly 
renewing the difference of potential. At the same time 
it will be noticed that a few bubbles of hydrogen gas 
appear on the surface of the copper plate. Both these 
actions go on as long as the wires are joined to form a 
complete cu'cuit. The metallic zinc may be considered 
as a store of energy. We know that if burned as a fuel 
in oxygen or air it wiU. give out that store of energy as 
heat. If burned in this qaiet chemical manner in a 
cell it gives out its store not as heat — any heat in a cell 
is so much waste — but in the form of electric energy, 
i.e. the energy of an electric cm'rent propelled by an 
electromotive force. 

167. Effects produced by Current. — The current 
itself cannot be seen to flow through the wire circuit ; 
hence to prove that any particular cell or combination 
produces a current requires a knowledge of some of the 
effects which currents can produce. These are of various 
kinds. A current flowing through a thin wire will heat 
it; flowing near a magnetic needle it will cause it to 
turn aside ; flowing through water and other liquids it 
decomposes them ; and, lastly, flowing through the living 
body or any sensitive portion of it, it produces certain 
sensations. These effects, thermal, magnetic, chemical, 
and physiological, will be considered in special lessons. 

168. Voltaic Battery. — If a number of such simple 
cells are united in series, the zinc plate of one joined to 
the copper plate of the next, and so on, a greater differ- 
ence of potentials will be produced between the copper 
" pole " at one end of the series and the zinc " pole " at 
the other end. Hence, when the two poles are joined 
by a wire there will be a more powerful flow of electricity 
than one cell would cause. Such a combination of 
Yoltaic Cells is called a Voltaic Battery.* There are 

* By some writers the name Galvanic Battery is given in honour of 
Galvani ; but the honour is certainly Yolta's. The electricity that flows 
thus in currents is sometimes called Voltaic Electricity, or Galvanic 



154 ELECTEICITY AND MAGNETISM part i 

many waj's of grouping a battery of cells, but two need 
special notice. If the cells are joined up in one row, 
as in Fig. 96 or Fig. 98, they are said to be in series. 
Electricians often represent a cell by a symbol in which 

a short thick line stands for 

II I j the zinc and a longer thin 

_lL|Li| ^^t. line for the copper (or car- 
■[ "I "I bon). Thus Fig. 98 repre- 

pjo. 98. sents four cells joined in 

series. So joined they do 
not yield more current (mpre amperes) than a single cell 
would yield, but they yield that current with a fourfold 
electromotive force {i.e. with more volts of pressure). 

The other chief way of grouping cells is to join all 
the zincs together and all the coppers (or carbons) to- 
gether ; and they are then 
said to be in parallel, or are 
joined "for quantity." So 
joined they have no greater 
electromotive - force than 
one cell. The zincs act like -^w 99. 

one big zinc, the coppers 

like one big copper. But they will yield more current. 
Fig. 99 shows the four cells grouped in parallel; they 
would yield thus a cm-rent four times as great as one cell 
alone would yield. 

169. Electromotive-Force. — The term electromotive- 
force is employed to denote that which moves or tends 
to move electricity from one place to another.* For 

Electricity, or sometimes even Galvanism (!), but, as we shall see, it differs 
only in degree from Frictional or any other Electricity, and both can flow 
along wires, and magnetize ii-on, and decompose chemical compounds. 
The word Battery means an arrangement of one or more cells ; just as in 
warfare a battery of guns meaus an arrangement of one or more. 

* The beginner must not confase Electromotive-force, or that which 
tends to move electricity, with Electric ''force,'" or that force with which 
electricity tends tq move matter. Newton has virtually defined "force," 
once for all, as that which moves or tends to move matter. When matter 
is moved by a magnet we speak rightly of magnetic force ; when electricity 




CHAP. Ill ELECTROMOTIVE EORCE ' 155 

brevity we sometimes write it E.M.F. In this particular 
case it is obviously the result of the difference of poten- 
tial, and proportional to it. Just as in water-pipes a 
difference of level produces a pressure, and the pressure 
produces 2ifiow so soon as the tap is turned on, so cUffer- 
ence of potential produces eleciromotiveforce, and electro- 
motive-force sets up a current so soon as a circuit is 
completed for the electricity to flow through. Electro- 
motive-force, therefore, may often be conveniently ex- 
pressed as a difference of potential, and vice versa; but 
the student must not forget the distinction. The unit in 
which electromotive-force is measured is termed the volt 
(see Art. 351:). The teYias, pressure and voltage are some- 
times used for difference of potential or electromotive-force. 
• 170 Volta's Laws. — Volta showed (Art. 79) that 
the difference of potential between two metals in contact 
(in ah') depended merely on what metals they were, not 
on their size, nor on the amount of surface in contact. 
He also showed that when a number of metals touched 
one another the difference of potential between the first 
and last of the row is the same as if they touched one 
another directly. A quantitative illustration from the 
researches of Ayrton and Perry was given in Art. 80. 
But the case of a series of cells is different from that of 
a mere row of metals in contact. If in the row of cells 
the zincs and coppers are all arranged in one order, so 
that all of them set up electromotive-forces in the same 
direction, the total electromotive-force of the series will he 
equal to the electromotive-fay^ce of one cell multiplied by the 
number of cells. 

Hitherto we have spoken only of zinc and copper as 
the materials for a cell ; but cells may be made of any 
two metals. The effective electromotive-force of a cell 
depends on the difference between the two. If zinc was 

moves matter we may speak of eZec^ric/orce. But E.M.F. is quite a dif- 
ferent thing, not " force " at all, for it acts not on matter but on electricity, 
and tends to move it. 



156 ' ELECTRICITY AND MAGNETISM part i 

used for both metals in a cell it would give no current, 
for each plate would be trying to dissolve and to throw a 
current across to the other with equal tendency. That 
cell will have the greatest electromotive-force or be the 
most " intense," in which those materials are used which 
have the greatest difference in their tendency to combine 
chemically with the acid, or which are widest apart on 
the " contact-series " given in Art. 80. Zinc and copper 
are convenient in this respect ; and zinc and silver would 
be better but for the expense. For more powerful bat- 
teries a zinc-platinum or a zinc-carbon combination is 
preferable. That plate or piece of metal in a cell by 
which the current enters the liquid is called the anode ; 
it is that plate which dissolves away. The plate or piece 
of metal by which the current leaves the cell is called the 
kathode ; it is not dissolved, and in some cases receives 
a deposit on its surface. 

171. Resistance. — The same electromotive - force 
does not, however, always produce a current of the same 
strengtli. The amount of current depends not only on 
the force tending to drive the electricity round the 
circuit, but also on the resistance which it has to 
encounter and overcome in its flow. If the cells be 
partly choked with sand or sawdust (as is sometimes 
done in so-called " Sawdust Batteries " to prevent spill- 
ing), or, if the wire provided to complete the circuit 
be very long or very thin, the action will be partly 
stopped, and the current will be weaker, although the 
E.M.F. may be unchanged. The analogy of the water- 
pipes will again help us. The pressure which forces the 
water through pipes depends upon the difference of level 
between the cistern from which the water flows and the 
tap to which it flows ; but the amount of water that 
runs through will depend not on the pressure alone, but 
on the resistance it meets with; for, if the pipe be a 
very thin one, or choked with sand or sawdust, the water 
will only run slowly through. 



CHAP. Ill CHEMICAL ACTIONS 157 

Xow the metals in general conduct well : their resist- 
ance is small ; but metal wires must not be too thin or 
too long, or they will resist too much, and permit only a 
feeble current to pass through them. The liquids in the 
cell do not conduct nearly so well as the metals, and dif- 
ferent liquids have different resistances. Pure water will 
hardly conduct at all, and is for the feeble electricity of 
the voltaic battery almost a perfect insulator, though for 
the high-potential electricity of the frictional machines it 
is, as we have seen, a fair conductor. Salt and saltpetre 
dissolved in water are good conductors, and so are dilute 
acids, though strong sulphuric acid is a bad conductor. 
The resistance of the liquid in the cells may be reduced, 
if desired, by using larger plates of metal and putting 
them nearer together. Gases are bad conductors ; hence 
the bubbles of hydrogen gas which are given off at the 
copper plate during the action of the cell, and which stick 
to the surface of the copper plate, increase the internal 
resistance of the cell by diminishing the effective surface 
of the plates. 

Lesson XIY. — Chemical Actions in the Cell 

172. Chemical Actions. — The production of a cur- 
rent of electricity by a voltaic cell is always accompanied 
by chemical actions in the cell. One of the metals at 
least must be readily oxidizable, and the liquid must be 
one capable of acting on the metal. As a matter of 
fact, it is found that zinc and the other metals which 
stand at the electropositive end of the contact-series (see 
Art. 80) are oxidizable ; whilst the electronegative sub- 
stances — copper, silver, gold, platinum, and graphite — 
are less oxidizable, and the last three resist the action of 
every single acid. There is no proof that their electri- 
cal behaviour is due to their chemical behaviour; nor 
that their chemical behaviour is due to their electrical, 



158 ELECTRICITY AND MAGNETISM part i 

Probably both result from a common cause (see Art. 80, 
and also 489). A piece of quite pm-e zinc when dipped 
alone into dilute sulphmic acid is not attacked by the 
liquid. But the ordinary commercial zinc is not pure, 
and when pluuged into dilute sulphuric acid dissolves 
away, a large quantity of bubbles of hydi'ogen gas being- 
given off fi'om the surface of the metal. Sulphmic acid 
is a complex substance, in which every molecule is made 
up of a group of atoms — 2 of Hydrogen, 1 of Sulphur, 
and 4 of Oxygen ; or, in symbols, H2SO4. The chemical 
reaction by which the zinc enters into combination with 
the radical of the acid, turning out the hydrogen, is 
expressed in the following equation : — 



Zn 


+ H2SO, 


ZnSO^ 


+ 


H, 


Zinc 


and Sulpliui'ic Acid produce 


Sulpliate of Zinc 


and 


Hydrogen. 



The sulphate of zinc produced in this reaction remains in 
solution in the liquid. 

Xow, when a plate of pure zinc and a plate of some 
less-easily oxidizable metal — copper or platinum, or, best 
of all, carbon (the hard carbon from gas retorts) — are 
put side by side into the cell containing acid, no appre- 
ciable chemical action takes place until the cii'cuit is com- 
pleted by joining the two plates with a wire, or by makmg 
them touch one another. Directly the cu'cuit is com- 
pleted a current flows and the chemical actions begin, 
the zinc dissolving m the acid, and the acid giving up its 
hydrogen in streams of bubbles. But it will be noticed 
that these bubbles of hydrogen are evolved not at the 
zinc plate, nor yet thi'oughout the liquid, but at the sur- 
face of the copper plate (or the carbon plate if carbon is 
employed).- This apparent transfer of the hydrogen 
gas through the liquid from the surface of the zinc plate 
to the smiace of the copper plate where it appears is very 
remarkable. The ingenious theory fi-amed by Grotthuss 
to account for it, is explained in Lesson XL VII, on 
Electro-Chemistry. 



CHAP. Ill LOCAL CHEMICAL ACTIONS 159 

These chemical actions go on as long as the current 
passes. The quantity of zinc used up in each cell is pro- 
portional to the amount of electricity which flows round 
the circuit while the battery is at work; or, in other 
words, is proportional to the current. The quantity of 
hydrogen gas evolved is also proportional to the amount 
of zinc consumed, and also to the current. After the 
acid has thus dissolved zinc in it, it will no longer act 
as a corrosive solvent ; it has been " killed," as workmen 
say, for it has been turned into sulphate of zinc. The 
battery will cease to act, therefore, either when the zinc 
has all dissolved away, or when the acid has become 
exhausted, that is to say, when it is all turned into sul- 
phate of zinc. Stout zinc plates will last a long time, 
but the acids require to be renewed frequently, the spent 
liquor being emptied out. 

173. Local Action. — When the circuit is not closed 
the current cannot flow, and there should be no chemical 
action so long as the battery is producing no current. 
The impure zinc of commerce, however, does not re- 
main quiescent in the acid, but is continually dissolving 
and giving off hydrogen bubbles. This local action, 
as it is termed, is explained in the following manner : — 
The impurities in the zinc consist of particles of iron, 
arsenic, and other metals. Suppose a particle of iron to 
be on the surface anywhere and in contact with the acid. 
It will behave like the copper plate of a battery towards 
the zinc particles in its neighbourhood, for a local differ- 
ence of potential will be set up at the point where there 
is metallic contact, causing a local or parasitic current to 
run from the particles of zinc through the acid to the 
particle of iron, and so there will be a continual wasting 
of the zinc, both when the battery circuit is closed and 
when it is open. 

174. Amalgamation of Zinc. — We see now why a 
piece of ordinary commerical zinc is attacked on being 
placed in acid. There is local action set up all over its 



160 ELECTEICITY AXD MAGNETISM pakt i 

surface in consequence of the metallic impurities in it. 
To do away with this local action, and abolish the 
wasting of the zinc while the battery is at rest, it is 
usual to amalgamate the surface of the zinc plates with 
mercury. The surface to be amalgamated should be 
cleaned by dipping into acid, and then a few drops of 
mercury should be poured over the sm'face and rubbed 
into it with a bit of linen rag tied to a stick. The 
mercury unites with the zinc at the surface, forming a 
pasty amalgam. The iron particles do not dissolve in 
the mercury, bat float up to the surface, whence the 
hydrogen bubbles which may form speedily carry them 
off. As the zinc in this pasty amalgam dissolves into 
the acid the film of mercury unites with fresh portions 
of zinc, and so presents always a clean bright sui'face to 
the liquid. 

A newer and better process is to add about 4 per cent 
of mercmy to the molten zinc before casting into plates 
or rods. If the zinc plates of a battery are well amal- 
gamated there should be no evolution of hydrogen bub- 
bles when the cu'cuit is open. Nevertheless there is still 
always a little wasteful local action dm*ing the action of 
the battery. Jacobi found that while one part of hydro- 
gen was devolved at the kathode, 33-6 parts of zinc were 
dissolved at the anode, instead of the 32-5 parts which 
are the chemical equivalent of the hydrogen. 

175. Polarization. — The bubbles of hydrogen gas 
liberated at the surface of the copper plate stick to it in 
great numbers, aud form a film over its surface.; hence 
the effective amount of surface of the copper plate is 
very seriously reduced in a short time. When a simple 
cell, or battery of such cells, is set to produce a current, 
it is found that the current after a few minutes, or even 
seconds, falls off very greatly, and may even be almost 
stopped. This immediate falling off in the current, 
which can be observed with any galvanometer and a 
pair of zinc and copper plates dipping into acid, is 



CHAP. Ill POLARIZATION IN CELLS 161 

almost entii-ely due to the film of hydrogen bubbles 
sticking to the copper pole. A battery which is in this 
condition is said to be " polarized." 

176. Effects of Polarization. — The film of hydrogen 
bubbles affects the strength of the current of the cell in 
two ways. 

Firstly, it weakens the current by the increased resist- 
ance which it offers to the flow, for bubbles of gas are bad 
conductors ; and, worse than this, 

Secondly, it weakens the current by setting up an 
opposing electromotive-force; for hydrogen is almost as 
oxidizable a substance as zinc, especially when it is being 
deposited (or in a " nascent " state), and is electropositive, 
standing high in the series on p. 85. Hence the hydro- 
gen itself produces a difference of potential, which would 
tend to start a current in the opposite direction to the 
true zinc-to-copper current. No cell in which the polari- 
zation causes a rapid falling off in power can be used for 
closed circuit work. 

It is therefore a very important matter to abolish this 
polarization, otherwise the currents furnished by batteries 
would not be constant. 

177. Remedies against Internal Polarization. — Vari- 
ous remedies have been practised to reduce or prevent 
the polarization of cells. These may be classed as 
mechanical, chemical, and electrochemical. 

1. Mechanical Means. — If the hydrogen bubbles be 
simply brushed away from the surface of the kathode, 
the resistance they caused will be diminished. If air 
be blown into the acid solution through a tube, or if 
the liquid be agitated or kept in constant circulation by 
siphons, the resistance is also diminished. If the surface 
be rough or covered with points, the bubbles collect more 
freely at the points and are quickly carried up to the 
surface, and so got rid of. This remedy was applied in 
Smee's Cell, which consisted of a zinc and a platinized 
silver plate dipping into dilute sulphuric acid ; the silver 



162 ELECTRICITY AXD MAGNETISM part i 

plate, having its surface thus covered with a rough coat- 
ing of finely divided platinum, gave up the hydrogen 
bubbles freely ; nevertheless, in a battery of Smee Cells 
the current diminishes greatly after a few minutes. 

2. Chemical Means. — If a highly-oxidizing substance 
be added to the acid it will destroy the hydrogen bubbles 
whilst they are still in the nascent state, and thus will 
prevent both the increased internal resistance and the 
opposing electromotive-force. Such substances are bi- 
chromate of potash, nitric acid, and chlorine. 

3. Electrochemical Means. — It is possible by employ- 
ing double cells, as explained in the next lesson, to so 
arrange matters that some solid metal, such as copper, 
shall be liberated instead of hydrogen bubbles, at the 
point where the current leaves the liquid. This electro- 
chemical exchange entirely obviates polarization. 

178. Simple Laws of Chemical Action in the Cell. — 
We will conclude this section by enumerating the two 
simple laws of chemical action in the cell. 

I. The amount of chemical action in the cell is propor- 
tional to the quantity of electricity that passes through it — 
that is to say, is proportional to the current while it 
passes. 

A current of one ampere flowing through the cell for 
one second causes 000083698 (or o-re:) ^^ ^ gramme of 
zinc to dissolve in the acid, and liberates 0-000010384 
(or Qslo o) of a gramme of hydrogen. 

IL The amount of chemical action is equal in each cell 
of a battery consisting of cells joined in series. 

The first of these laws was thought by Faraday, who 
discovered it, to disprove Volta's contact theory. He 
foresaw that the principle of the conservation of energy 
would preclude a mere contact force from furnishing a 
continuous supply of current, and hence ascribed the 
current to the chemical actions which were proportional 
in quantity to it. How the views of Volta and Faraday 
are to be harmonized has been indicated in the last 



CHAP. Ill VOLTAIC CELLS 163 

paragraph of Art. 80. These laws only relate to the 
useful chemical action, and do not include the waste of 
''local" actions (Art. 166) due to parasitic currents set 
up by impurities. 

Lesson XY. — Voltaic Cells 

179. A good Voltaic Cell should fulfil all or most of 
the following conditions : — 

1. Its electromotive-force should be high and con- 

stant. 

2. Its internal resistance should be small. 

3. It should give a constant current, and therefore 

must be free from polarization, and not liable 
to rapid exhaustion, requiring frequent renewal 
of the acid. 

4. It should be perfectly quiescent when the circuit 

is open. 

5. It should be cheap and of durable materials. 

6. It should be manageable, and if possible, should 

not emit corrosive fumes. 
!N"o single cell fulfils all these conditions, however, 
and some cells are better for one purpose and some for 
another. Thus, for telegraphing through a long line of 
wire a considerable internal resistance in the battery is 
no great disadvantage ; while, for producing an electric 
light, much internal resistance is absolutely fatal. The 
electromotive-force of a battery depends on the materials 
of the cell, and on the number of cells linked together, 
and a high E.M.F. can therefore be gained by choosing 
the right substances and by taking a large number of 
cells. The resistance within the cell can be diminished 
by increasing the size of the plates, by bringing them 
near together, so that the thickness of the liquid between 
them may be as small as possible, and by choosing liquids 
that are good conductors. 



164 ELECTRICITY AND MAGNETISM part i 

180. Classification of Cells. — Of the innumerable 
forms of cells that have been invented, only those of first 
importance can be described. Cells are sometimes classi- 
fied into two groups, according as they contain one or 
two fluids, or electrolytes, but a better classification is 
that adopted in Art. 177, depending on the means of pre- 
venting polarization. 

Class I. — With Mechaxical Depolarization. 
(Single Fluid.) 

The simple cell of Volta, with its zinc and copper 
plates, has been ah-eady described. The larger the cop- 
per plate, the longer time does it take to polarize. Cruick- 
shank suggested to place the plates vertically in a trough, 
producing a more powerful combination. Dr. "Wollaston 
proposed to use a plate of copper of double size, bent 
round so as to approach the zinc on both sides, thus 
diminishing the resistance, and allowing the hydrogen 
more surface to deposit upon. Smee, as we have seen, 
replaced the copper plate by platinized silver, and Walker 
suggested the use of plates of hard carbon instead of cop- 
per or silver, thereby saving cost, and at the same time 
increasing the electromotive-force. The roughness of the 
surface facilitates the escape of hydrogen bubbles. By 
agitating such cells, or raising their kathode plates for a 
few moments into the air, their power is partially restored. 
The Law cell, used in the United States for open-circuit 
work, is of this class : it has a small rod of zinc and a 
cleft cylinder of carbon of large surface immersed in 
solution of salammoniac. 

Class II. — With Chemical Depolarization. 

In these cells, in addition to the dilute acid or other 
excitant to dissolve the zinc, there is added some more 



CHAP. Ill EXCITANTS AND DEPOLARIZERS 



165 



powerful chemical agent as a depolarizer. Amongst de- 
polarizers the following are chiefly used : — Nitric acid, 
solutions of chromic acid, of bichromate of potash, of 
bichromate of soda, of nitrate of potash, or of ferric 
chloride; chlorine, bromine, black oxide of manganese, 
sulphur, peroxide of lead, red lead, oxide of copper. 
Most of these materials would, however, attack the 
copper as well as the zinc if used in a zinc-copper cell. 
Hence they can only 
be made use of in zinc- 
carbon or zinc-plati- 
num cells. Nitric acid 
also attacks zinc when 
the circuit is open. 
Hence it cannot be em- 
ployed in the same sin- 
gle cell with the zinc 
plate. In the Bichro- 
mate Cell, invented by 
Poggendorff, bichro- 
mate of potash is added 
to the sulpharic acid. 
This cell is most con- 
veniently niade up as 
shown in Fig. 100, in 
which a plate of zinc is 
the anode, and a pair 
of carbon plates, one on each side of the zinc, joined 
together at the top serve as a kathode. As this solution 
would attack the zinc even when the circuit is open, the 
zinc plate is fixed to a rod by which it can be drawn up 
out of the solution when the cell is not being worked. 

To obviate the necessity of this operation the device 
is adopted of separating the depolarizer from the liquid 
into which the zinc dips. In the case of liquid depola- 
rizers this is done by the use of an internal porous cell or 
partition. Porous cells of earthenware or of parchment 




Fig. 100. 



166 ELECTRICITY AXD MAGNETISM part i 

paper allow the electric current to flow while keeping the 
liquids apart. In one compartment is the zinc anode 
dipping into its aliment of dilute acid : in the other com- 
partment the carbon (or platinum) kathode dipping into 
the depolarizer. Such cells are termed two-Jluid cells. 
In the case of solid depolarizers such as black oxide of 
manganese, oxide of copper, etc., the material merely 
needs to be held up to the kathode. All solid depola- 
rizers are slow in acting. 

Class III. — ^Vith Electrochemical Depolariza- 

TIOX. 

When any soluble metal is immersed in a solution of 
its own salt — for example, zinc dipped into sulphate of 
zinc, or copper into sulphate of copper — there is a defi- 
nite electromotive-force between it and its solution, the 
measure of its tendency to dissolve. If a current is sent 
from metal to solution some of the metal dissolves ; if, 
however, the ciu'rent is sent from solution to metal some 
more metal will be deposited (or "plated") out of the 
solution. But as long as the chemical nature of the 
surface and of the liquid is unchanged there will be no 
change in the electromotive-force at the surface. It 
follows that if a cell were made with two metals, each 
dipping into a solution of its own salt, the two solutions 
being kept apart by a porous partition, such a ceD. would 
never change its electromotive-force. The anode would 
not polarize where it dissolves into the excitant; the 
kathode would not polarize, since it receives merely an 
additional thickness of the same sort as itself. This 
electrochemical method of avoiding polarization was dis- 
covered by Daniell. It is the principle not only of the 
DanieU cell, but of the Clark cell and of others. For per- 
fect constancy the two salts used should be salts of the 
same acid, both sulphates, or both chlorides, for example. 

181. DanieU's Cell. —Each cell or "element" of 



CHAP. Ill 



DANIELL'S CELL 



167 




Dauiell's battery has an inner porous cell or partition to 
keep the separate liquids from mixing. The outer cell 
(Fig. 101) is usually of copper, and serves also as a 
copper kathode. Within it is placed a cylindrical cell of 
unglazed porous ware (a cell of parchment, or even of 
brown paper, will answer), and in this is a rod of amalga- 
mated zinc as anode. The liquid 
in the inner cell is dilute sulphuric 
acid or dilute sulphate of zinc; 
that in the outer cell is a saturated 
solution of sulphate of copper 
(" blue vitriol "), some spare 
crystals of the same substance 
being contained in a perforated 
shelf at the top of the cell, in 
order that they may dissolve and 
replace that which is used up 
while the battery is in action. ^°' ^ ' 

When the circuit is closed the zinc dissolves in the 
dilute acid, forming sulphate of zinc, and liberating 
hydrogen ; but this gas does not appear hi bubbles on 
the surface of the copper cell, for, since the inner cell is 
porous, the molecular actions (by which the freed atoms 
of hydrogen are, as explained by Fig. 266, handed on 
through the acid) traverse the pores of the inner cell, and 
there, in the solution of sulphate of copper, the hydrogen 
atoms are exchanged for copper atoms, the result being 
that pure copper, and not hydrogen gas, is deposited on 
the outer copper plate. Chemically these actions may be 
represented as taking place in two stages. 

Zn + H2SO4 = ZnSO^ + H2 

Zinc and Sulphuric Acid produce Sulphate of Zinc and Hydrogen, 

And then 



H. 



CuSO. 



H2SO4 



Cu. 



Hydrogen and Sulphate of Copper produce Sulphuric Acid and Copper, 



168 ELECTRICITY AND :\IAGXETISM pakt i 

The hydrogen is, as it were, translated electro 
chemically into copper dnring' the ronnd of changes, 
and so while the zinc dissolves away the copper grows, 
the dilute sulphmic acid gradually changing into sul- 
phate of zinc, and the sulphate of copper into sulphuric 
acid. In the case in which a solution of sulphate of zinc 
is used there is no need to consider any hydrogen atoms, 
copper being exchanged chemically for zinc. There is 
therefore no polarization so long as the copper solution is 
saturated ; and the cell is very constant, though not so 
constant in all cases as Clark's standard cell described in 
Art. 188, owing to slight variations in the electromotive- 
force as the composition of the other fluid varies. When 
sulphuric acid diluted with twelve parts of water is used 
the E.M.F. is 1-178 volts. The E.M.F. is 1-07 volts when 
concentrated zinc sulphate is used ; 1-1 volts when a half- 
concentrated solution of zinc sulphate is used ; and, in 
the common cells made up with water or dilute acid, 
1-1 volts or less. Owing to its constancy, this battery, 
made up in a convenient flat form (Fig. 106), has been 
much used in telegraphy. It is indispensable in those 
"closed circuit" methods of telegraphy (Art. 500), where 
the current is kept always flowing until interrupted by 
signalling. 

182. Grove's Cell.— Sir William Grove devised a 
form of cell having both higher voltage and smaller 
internal resistance than Daniell's cell. In Grove's ele- 
ment there is an outer cell of glazed ware or of ebonite, 
containing the amalgamated zinc plate and dilute sul- 
phuric acid. In the inner porous cell a piece of platinum 
foil serves as the negative pole, and it dips into the 
strongest nitric acid. There is no polarization in this 
cell, for the hydrogen liberated by the solution of the 
zinc in dilute sulphuric acid, in passing through the 
nitric acid in order to appear at the platmum pole, de- 
composes the nitric acid and is itself oxidized, producing 
water and the red fumes of nitric peroxide gas. This 



CHAP. Ill GROVE'S CELL 169 

gas does not, however, produce polarization, for as it is 
very soluble in nitric acid, it does not form a film upon 
the face of the platinum plate, nor does it, like hydrogen, 
set up an opposing electromotive-force with the zinc. 
The Grove cells may be made of a flat shape, the zinc 
being bent up so as to embrace the flat porous cell on 
both sides. This reduces the internal resistance, which 
is already small on account of the good conducting 
powers of nitric acid. Hence the Grove cell will furnish 
for three or four hours continuously a strong current. 
The E.M.F. of one cell is about 1-9 volts, and its internal 
resistance is very low (about 0-1 ohm for the quart size). 
A single cell will readily raise to a bright red heat two 
or three inches of thin platinum wire, or drive a small 
electromagnetic engine. For producing larger power a 
number of cells must be joined up in series, the plat- 
inum of one cell being clamped to the zinc of the next 
to it. Fifty such cells, each holding about a quart of 
liquid, amply suffice to produce an electric arc light, as 
will be explained in Lesson XXXIX. 

183. Bunsen's Cell. — The cell which bears Bunsen's 
name is a modification of that of Grove, and was indeed 
originally suggested by him. In the Bunsen cell the 
expensive * platinum foil is replaced by a rod or slab of 
hard gas carbon. A cylindrical form of cell, with a rod 
of carbon, is shown in Fig. 102. The voltage for a zinc- 
carbon combination is a little higher than for a zinc- 
platinum one, which is an advantage ; but the Bunsen 
cell is troublesome to keep in order, and there is some 
difficulty in making a good contact between the rough 
surface of the carbon and the copper strap which connects 

* Platinum costs about 30 shillings an ounce — nearly half as much as 
gold ; while a hundredweight of the gas carbon may be had for a mere trifle, 
often for nothing more than the cost of carrying it from the gasworks. An 
artificial carbon prepared by grinding up gas carbon with some carbonaceous 
matter such as tar, sugar residues, etc., then pressing into moulds, and 
baking in a furnace, is used both for battery plates and for the carbon rods 
used in arc lamps. 



170 



ELECTRICITY AND MAGNETISM part i 



the carbon of one cell to the zinc of the next. The top 
part of the carbon is sometimes 
impregnated with paraffin wax to 
keep the acid from creeping up, 
and electrotyped with copper. 
Fig. 103 shows the usual way of 
coupling up a series of five such 
cells. The Bunsen's battery will 
continue to furnish a current for 
a longer time than the flat Grove's 
cells, on account of the larger 
quantity of acid contained by the 
cylindrical pots.* 

Chromic solutions, formed by 
adding strong sulphuric acid to 
solutions of bichromate of potash or of soda, are often 
used instead of nitric acid, in cells of this form. Soluble 




Fig. 102. 




Fig. 103. 



depolarizers in the form of chromic powders are made 
by heating strong sulphuric acid and gradually stirring 
into it powdered bichromate of soda. The pasty mass is 
then cooled and powdered. 



* Callan constructed a large battery in which cast-iron formed the 
positive pole, being immersed in strong nitric acid, the zincs dipping into 
dilute acid. The iron under these circumstances is not acted upon by the 
acid, but assumes a so-called " passive state." In this condition its surface 
appears to be impregnated with a film of magnetic peroxide, or of oxygen. 



CHAP. Ill 



LECLANCH:fe'S CELL 



171 



184. Leclanche's CelL — For working electric bells 
and telephones, and also to a limited extent in teleg- 
raphy, a zinc-carbon cell is employed, invented by Le- 
clanche, in which the exciting liquid is not dilute acid, but 
a solution of salammoniac. In this the zinc dissolves, 
forming a double chloride of zinc and ammonia, while 
ammonia gas and hydrogen are liberated at the carbon 
pole. The depolarizer is the black binoxide of manga- 
nese, fragments of which, mixed with powdered carbon, 
are held up to the carbon kathode either by packing them 
together inside a porous pot or by being attached as an 
agglomerated block. The oxide of manganese will slowly 




Fig-. 104. 



yield up oxygen as required. If used to give a continuous 
current for many minutes together, the power of this cell 
falls off owing to the accumulation of the hydrogen bub- 
bles ; but if left to itself for a time the cell recovers itself, 
the binoxide gradually destroying the polarization. As 
the cell is in other respects perfectly constant, and does 
not require renewing for months or years, it is well adapted 
for domestic purposes. It has the advantage of not con- 
taining corrosive acids. Millions of these cells are in use 
on " open-circuit " service — that is to say, for those cases 
in which the current is only required for a few moments 
at a time, and the circuit usually left open. Three 
Leclanche cells are shown joined in series, in Fig. 104. 



172 ELECTRICITY AND MAGNETISM part i 

Walker used sulphur in place of oxide of manganese. 
Maudet employed bleaching powder (so called chloride 
of lime) as depolarizer, it being rich in chlorine and oxy- 
gen. Common salt may be used instead of salammoniac. 
Modifications of the Leclanche cell in which the 
excitant cannot be spilled are used for portability. The 
space inside the cell is filled up with a spongy or gelati- 
nous mass, or even with plaster of Paris, in the pores of 
which the salammoniac solution remains. They are 
known as dry cells. 

185. Lalande's Cell. — This cell belongs to Class 11., 
having as depolarizer oxide of cop^Der mechanically at- 
tached to a kathode of copper or h'on. The anode is 
zinc, and the exciting liquid is a 30 per cent solution of 
caustic potash into which the zinc dissolves (forming 
zincate of potash), whilst metallic copper is reduced in a 
granular state at the kathode. It has only 0-8 to 0-9 
volts of E.M.F., but is capable of yielding a large and 
constant current. 

186. De la Rue's Battery. — De la Rue constructed 
a constant cell belonging to Class III., in which zinc and 
silver are the two metals, the zinc being immersed in 
chloride of zinc, and the silver embedded in a stick of 
fused chloride of silver. As the zinc dissolves away, 
metallic silver is deposited upon the kathode, just as the 
copper is in the Daniell's cell. De la Rue constructed 
an enormous battery of over 11,000 little cells. The 
difference of XDotential between the first zinc and last 
silver of this battery was over 11.000 volts, yet 
even so no spark would jump fi'om the 4- to the — 
pole until they w^ere brought to within less than a 
quarter of an inch of one another. With 8040 cells 
the length of spark was only 0-08 of an inch, or 
0-2 cm. 

187. Gravity Cells. — Instead of employing a porous 
cell to keep the two liquids separate, it is possible, where 
one of the liquids is heavier thun the other, to arrange 



CHAP. Ill CLAKK'S STANDARD CELL 



173 



that the heavier liquid shall form a stratum at the 
bottom of the cell, the lighter floating upon it. Such 
arrangements are called graviti/ cells ; but the separation 
is never perfect, the heavy liquid slowly diffusing up- 
wards. Daniell's cells arranged as gravity cells have 
been contrived by Meidinger, Minotto, Callaud, and Lord 
Kelvin. In Siemens' modification paper-pulp is used 
to separate the two liquids. The " Sawdust Battery " 
of Kelvin is a Daniell's battery, having the cells filled 
with sawdust, to prevent spilling and make them 
portable. 

188. Clark's Standard Cell. — A standard cell whose 
E.M.F. is even more constant than that of the Daniell 
was suggested by Latimer 
Clark. This cell, which is 
now adopted as the inter- 
national standard cell, con- 
sists of an anode of pure 
zinc in a concentrated solu- 
tion of zinc-sulphate, whilst 
the kathode is of pure mer- 
cury in contact with a paste 
of mercurous sulj)hate. Pre- 
cise instructions for setting 
up Clark cells are given 
in Appendix B at the end 
of this book. Fig. 105 
shows, in actual size, the 
form of the Clark cell. 
15° C. 

Weston uses a cadmium anode immersed in sulphate 
of cadmium and finds the cell so modified to give 1-025 
volts at all ordinary temperatures. 

Von Helmholtz has used mercurous chloride (calomel) 
and chloride of zinc, in place of sulphates, in a standard 
cell. Carhart finds its E.M.F. (a little over 1 volt) to 
vary with the dilution of the chloride of zinc. 




Fig. 105. 

Its E.M.F. is 1431 volts at 



174 



ELECTRICITY AND MAGNETISM part 



189. Statistics of Cells. — The following table gives 
the electromotive-forces of the various batteries enu- 
merated : — 













Approxi- 


jSTame. 


Anode. 


Excitant. 


Depolarizer. 


Kathode. 


mate 
Yolts. 


Class I. 




(Solution of) 








Volta (WoUaston, 


Zinc 


H2SO4 


none 


Copper 


1-0 to 0-5 


etc.) , 












Smee 


Zinc 


H2SO4 


none 


Platinized 
Silver 


1-0 to 0-5 


Law 


Zinc 


H3SO4 


none 


Carbon 


1-0 to 0-5 


Class 11. 












Poggendorff (Gre- 


Zinc 


H2SO4 


KjCrgO^ 


Carbon 


2-1 


net, Fuller, etc.). 












Grove 


Zinc 


H2SO4 


HN-Qs 


Platinum 


1-9 


Bunsen . 


Zinc 


H,S0j 


HJ^Og 


Carbon 


1-9 


Leclancbe 


Zinc 


NH4CI 


MnOj 


Carbon 


1-4 


Lalande . 


Zinc 


KHO 


CuO 


Carbon 


0-8 


Upward . 


Zinc 


ZnClj 


CI 


Carbon 


2-0 


Fitch . 


Zinc 


NH4CI 


KClOo+Na 












CIO3 


Carbon 


1-1 


Papst . 


Iron 


Fe^Clo 


FeaCle 


Carbon 


0-4 


Obach(dry) . . 


Zinc 


NH4CI 
in CaSO^ 


MnOj 


Carbon 


1-46 


Class III. 












DanieU(Meidinger, 


Zinc 


ZnSOi 


CuSO^ 


Copper 


1-07 


Minotto, etc.) . 












De la Eue . 


Zinc 


ZnCl2 


AgCl 


Silver 


1-42 


Marie Davy . 


Zinc 


ZnSOi 


Hg2S04 


Carbon 


1-4 


Clark (Standard) . 


Zinc 


ZnS04 


HgaSO^ 


Mercury 


1-434 


Weston . 


Cadmium 


CdSO. 


Hg2S04 


Mercury 


1-025 


Von Helmholtz 


Zinc 


ZnCl, 


Hg,C]3 


Mercury 


1-0 


Class IV. 












Accumulators. 












(Plaiite, Faiire,etc.) 


Lead 


BSO, 


PbOj 


Lead 


2-1 to 1-85 



190. Strength of Current. — The student must not 
mistake the figures given in the above table for the 
strength of current which the various batteries will 
yield ; the current depends, as was said in Lesson XIIL, 
on the internal resistance of the cells and on that of their 



CHAP. Ill OHM'S LAW 175 

circuit, as ^Yell as on their E.M.F. The E.M.F. of a cell 
is independent of its size, and is determined solely by the 
materials chosen and their condition. The resistance 
depends on the size of the cell, the conducting qualities 
of the liquid, the thickness of the liquid which the cur- 
rent must trayerse, etc. 

The definition of the strength of a current is as fol- 
lows : The strength of a current is the quantity of electricity 
which flows past any point of the circuit in one second.* 
Suppose that at the end of 10 seconds 25 coulombs of 
electricity to have passed through a circuit, then the 
average current during that time has been 2^ coulombs 
per second, or 2% amperes. The usual strength of currents 
used in telegraphing over main lines is only from five to 
ten thousandths of an ampere. 

If in t seconds a quantity of electricity Q has flowed 
through the circuit, then the current C during that time 
is represented by the equation 

This should be compared with Art. 162. 

The laws which determine the strength or quantity of 
a current in a circuit wei'e first enunciated by Dr. G. S. 
Ohm, who stated them in the following law : — 

191. Ohm's Law. — The current varies directly as the 
electromotive-force, and inversely as the resistance of the 
circuit; or, in other words, anything that makes the 

* The terms "strength of current," "intensity of current," are old- 
fashioned, and mean no more than "current" means — that is to say, the 
number of amperes that are tiowing. The terms " strong," "great," and 
" intense," as appUed to currents, mean precisely the same thing. Formerly, 
before Ohm's Law was properly understood, electricians used to talk about 
"quantity cun-ents" and " intensity currents," meaning by the former 
term a current flowing through a circuit in which there is very small 
resistance inside the battery or out ; and by the latter expression they 
designated a current due to a high electromotive-force. The terms were 
convenient, but should be avoided as misleading. 



176 ELECTRICITY AND MAGNETISM part i 

E.M.F. of the cell greater will increase the current, while 
anything that increases the resistance (either the internal 
resistance in the cells themselves or the resistance of the 
external wires of the circuit) will diminish the current. 
In symbols this becomes <■ 

where E is the number of volts, R the number of ohms 
of the circuit, and C the number of amperes of current. 

Example. — To find the current that can be sent through a 
resistance of 5 ohms by an E.M.F. of 20 volts. 20 -^ 5 = 4 
amperes. 

(See further concerning Ohm's Law in Lesson XXXIII.) 
Ohm's Law says nothing about the energy or power con- 
veyed by a current. The power of a current is propor- 
tional both to the current and to the electromotive-force 
which drives it (see Art. 435). 

192. Resistance and Grouping of Cells. — The inter- 
nal resistances of the cells we have named differ very 
greatly, and differ with their size. Roughly speaking, 
we may say that the resistance in a Daniell's cell is 
about five times that in a Grove's cell of equal size. 
The Grove's cell has indeed both a higher E.M.F. and 
less internal resistance. It would in fact send a current 
about eight times as strong as the Daniell's cell of equal 
size through a short stout wu-e. 

We may then increase the strength of a battery in 
two ways : — 

(1) By increasing its E.M.F. 

(2) By diminishing its internal resistance. 

The electromotive-force of a cell being determined by 
the materials of which it is made, the only way to in- 
crease the total E.M.F. of a battery of given materials 
is to increase the number of cells joined "in series." It 



CHAP. Ill RESISTANCE OF CELLS 177 

is frequent in the telegraph service to link thus together 
two or three hundred of the flat Darnell's cells; and they 
are usually made up in trough-like boxes, containing a 
series of 10 cells, as shown in Fig. 106. 

To diminish the internal resistance of a cell the follow- 
ing expedients may be resorted to : — 

(1) The plates may be brought nearer together, so 
that the current shall not have to traverse so thick a 
stratum of liquid. 

(2) The size of the plates may be increased, as this 




affords the current, as it were, a greater number of pos- 
sible paths through the stratum of liquid. 

(3) The zincs of several cells may be joined together, 
to form, as it were, one large zinc plate, the coppers being 
also joined to form one large copper plate. Suppose four 
similar cells thus joined " in parallel," the current has four 
times the available number of paths by which it can 
traverse the liquid from zinc to copper ; hence the in- 
ternal resistance of the whole will be only ^ of that of 
a single cell. But the E.M.F. of them will be no greater 
thus than that of one cell. 

It is most important for the student to remember that 
the current is also affected by the resistances of the wires 
of the external circuit ; and if the external resistance be 



178 ELECTRICITY AXD MAGNETISM part i 

already great, as in telegraphiug thj-ough a long Une, it 
is little use to diminish the internal resistance if this is 
already much smaller than the resistance of the line wire. 
It is, on the contrary, adyantageous to increase the num- 
ber of cells in series, though eyery cell adds a little to the 
total resistance. 

Example. — ^ the line has a resistance of 1000 ohms, and five 
cells are used each of which has an E.M.F. of 1*1 voJt 
and an internal resistance of 3 ohms. By Ohm's La"^ 
the current wiU be 5"5 -^ 1015 ; or 00051 amjjere. If 
now eight cells are used, though the total resistance is 
thereby increased from 1015 to 1010 ohms, yet the 
E.M.F. is increased from 5'5 to 8'8 volts, and the 
current to 0"0085 ampere. 

The E.M.F. of the single-fluid cells of Volta and Smee 
is marked in the table as doubtful, for the opposing 
E.M.F. of polarization sets in almost before the true 
E.M.F. of the cell can be measured. The different yalues 
assigned to other cells are accounted for by the different 
degrees of concentration of the liquids. Thus in the 
Daniell's cells used in telegTaphy, water only is supplied 
at first in the cells containing the zincs : and the E.M.F. 
of these is less than if acid or sulphate of zinc were added 
to the water. 

193. Other Batteries. — Xumei-ous other forms of 
battery have been suggested by different electidcians. 
There are three, of theoretical interest only, in which, 
instead of using two metals in one liquid which attacks 
them unequally, two liquids are used haying unequal 
chemical action on the metal. In these there is no con- 
tact of dissimilar metals. The first of these was inyented 
by the Emperor Xapoleon III. Both plates were of cop- 
per dipping respectiyely into solutions of dilute sulphuric 
acid and of cyanide of potassium, separated by a porous 
cell. The second of these combinations, due to AVohler, 
employs plates of aluminium only, dipping respectiyely 
into strong nitric acid ancl a solution of caustic soda. In 



CHAP. Ill MISCELLANEOUS CELLS 179 

the thii'd, invented by Dr. Fleming, the two liquids do 
not even touch one another, being joined together by a 
second metal. In this case the liquids chosen are sodium 
persulphide and nitric acid, and the two metals copper 
and lead. A similar batter}^ might be made with copper 
and zinc, using solutions of ordinary sodium sulphide, and 
dilute sulphuric acid in alternate cells, a bent zinc plate 
dipping into the first and second cells, a bent copper plate 
dipping into second and third, and so on ; for the electro- 
motive-force of a copper-sodium-sulphide-zinc combination 
is in the reverse direction to that of a copper-sulphuric 
acid-zinc combination. 

L'pward pro]Dosed a chlorine battery, having slabs of 
zinc immersed in chloride of zinc and kathodes of carbon 
surrounded by crushed carbon in a porous pot, gaseous 
chlorine being pumped into the cells, and dissolving into 
the liquids to act as a depolarizer. It has an E.M.F. of 
2 volts. 

Bennett described a cheap and most efficient battery, 
in which old meat-canisters packed with iron filings 
answer for the positive element, and serve to contain 
the exciting liquid, a strong solution of caustic soda. 
Scrap zinc thrown into mercury in a shallow inner cup 
of porcelain forms the anode. 

Marie Davy einployed a cell in which the zinc dipped 
into sulphate of zinc, while a carbon plate dipped into a 
pasty solution of mercurous sulphate. When the cell is 
in action mercury is deposited on the surface of the car- 
bon, so that the cell is virtually a zinc-mercury cell. It 
was largely used for telegraphy in France before the 
introduction of the Leclanche cell. 

Obach's dry cell has an outer cylinder of zinc which 
serves as a case, lined with plaster of Paris soaked in 
salammoniac ; with a central carbon kathode surrounded 
with binoxide of manganese mixed with graphite. 

The Fitch cell, used in the United States, is a zinc- 
carbon cell with an excitant composed of salammoniac 



180 ELECTEICITY AND ]MAGXETISM part i 

solution to which the chlorates of potash and soda have 
been added. 

Papst used an iron-carbon cell vrith ferric chloride 
solution as excitant. The h'on dissolves and chlorine is 
at first evolved, but without polarization ; the liquid 
regenerating itself by absorbing moisture from the air. 
It is very constant but of low E.M.F. 

Jablochkofl: described a battery in which plates of 
carbon and iron are placed in fu^d nitre ; the carbon is 
here the electropositive element /being rapidly consumed 
in the liquid. 

Plante's and Faure's Secondary Batteries, and Grove's 
Gas Battery, are described in Arts. 492, 493. 

The so-called Dry Pile of Zamboni deserves notice. 
It consists of a number of paper disks, coated with zinc- 
foil on one side and with binoxide of manganese on the 
other, piled upon one another, to the number of some 
thousands, in a glass tube. Its internal resistance is 
enormous, as the internal conductor is the moisture of 
the paper, and this is slight ; but its electromotive-force 
is very great, and a good dry pile will yield sparks. 
Many years may elapse before the zinc is comjjletely 
oxidized or the manganese exhausted. In the Clarendon 
Laboratory at Oxford there is a dry pile, the poles of 
which are two metal bells : between them is hung a small 
brass ball, which, by oscillating to and fro, slowly dis- 
charges the electrification. It has now been contuiuously 
ringing the bells for fifty years. 

194. Effect of Heat on Cells. — If a cell be warmed 
it yields a stronger cm-rent than when cold. This is 
chiefly due to the fact that the liquids conduct better 
when warm, the internal resistance being thereby reduced. 
A slight change is also observed in the E.M.F. on heat- 
ing ; thus the E.M.F. of a Daniell's cell is about 1^^ per 
cent higher when warmed to the temperature of boiling 
water, while that of a bichromate battery falls off 
nearly 2 per cent under similar circumstances. In the 



CHAP. Ill MAGNETIC EFEECTS OF CURRENT 181 

Clark standard cell the E.M.F. decreases slightly with 
temperature, the coefficient being 0-00077 per degrees 
centigrade. Its E.M.F. at any temperature may be 
calculated by the formula, 

E.IM.F. = 1434: [1 - 0-00077 {6 - 15) ] volt. 



Lessox XVI. — Magnetic Actions of the Current 

195. Oersted's Discovery. — A connexion of some 
kind betvveen magnetism and electricity had long been 
suspected. Lightning had been known to magnetize 
knives and other objects of steel; but almost all attempts 
to imitate these effects by powerful charges of electricity, 
or by sending currents of electricity through steel bars, 
had failed.* About 1802 Romagnosi, of 3^¥eate, vaguely 
observed that a voltaic pile affects a compass-needle. 'vv^v-^-t--<j>w ' 
The true connexion between magnetism and electricity 7V^>**^«v 
remained, however, to be discovered. 

In 1819, Oersted, of Copenhagen, showed that a mag- 
net tends to set itself at right angles to a wire carrying an 
electric current. He also found that the way in which 
the needle turns, whether to the right or the left of its 
usual position, depends upon the position of the wire that 
carries the current — whether it is above or below the 
needle, — and on the direction in which the current flows 
through the wire. 

196. Oersted's Experiment. — Very simple appara- 
tus suffices to repeat the fundamental experiment. Let 
a magnetic needle be suspended on a XDointed pivot, as 
in Fig. 107. Above it, and parallel to it, is held a stout 

* Down to this point in these lessons there has been no connexion 
between magnetism and electricity, though something has been said about 
each. The student who cannot remember Avhether a charge of electricity 
does or does not affect a magnet, should turn back to what was said in 
Art. 99. 






) 



182 



ELECTRICITY AXD MAGNETISM part i 



copper wire, one end of which is joined to one pole of a 
battery of one or two cells. The other end of the wire 
is then brought into contact with the other pole of the 
battery. As soon as the circuit is completed the current 
flows through the wire and the needle turns briskly aside. 
If the current be flowing along the wire above the needle 
in the direction from north to south, it will cause the 
X-seeking end of the needle to turn eastwards ; if the 
current flows from south to north in the wire the X-seek- 




Fi?. 10"; 



ing end of the needle will be deflected westwards. If the 
wire is, however, below the needle, the motions will be 
reversed, and a current flowing from north to south will 
cause the X-seeking pole to turn westwards. 

197. Ampere's Rule. — To keep these movements in 
memory. Ampere suggested the following fanciful but 
useful rule. Suppose a man swimming in the wire with 
the current, and that he turns so as to face the needle, then 
the X-seeking pole of the needle will be deflected towards his 
left hand. In other words, the deflexion of the X-seeking 
pole of a magnetic needle, as viewed from the conductor, 
is towards the left of the current. 

For certain particular cases in which a fxed magnet 
pole acts on a movable cii'cuit, the following converse to 



CHAP. Ill 



GALVAXOSCOPE 



183 




Ampere's Rule will be found convenient. Suppose a man 
swimming in the wire with the current, and that he turns 
so as to look along the direction of the lines of force of 
the pole (i.e. as the lines of force run,/rom the pole if it 
be X-seeking, towards the pole if it be S-seeking), then he 
and the conducting wire with him will be urged toward 
his left. 

198. Corkscrew Rule. — More convenient is the fol- 
lowing rule suggested by Maxwell. The direction of the 
current and that of the resulting magnetic force are related 
to one another, as are the rotation and 

the forward travel of an ordinary (right- 
handed) corkscrew. In Fig. 108, if the 
circle represents the circulation of current, 
the arrow gives the direction of the result- 
ing magnetic force. One advantage of 
this rule is, that it is equally applicable 
in the other case. If the arrow represents the direction 
of the current along a straight wire, the circle will 
represent the direction of the resulting magnetic force 
around it. 

199. Galvanoscope. — A little consideration will 
show that if a current be carried ielow a needle in one 

direction, and then back in the opposite 
direction ahove the needle, by bending 
the wire round, as in Fig. 109, the 
forces exerted on the needle by both 
portions of the current will be in the 
same direction. For let a be the 
I^-seeking, and h the S-seeking, -pole 
of the suspended needle, then the 
tendency of the current in the lower 
part of the wire wiU be to turn the 
needle so that a comes towards the observer, while h 
retreats ; while the current flowing above, which also 
deflects the N-seeking pole to its left, will equally urge 
a towards the observer, and h from him. The needle 




184 ELECTRICITY AND MAGNETISM part i 

will not stand ont completely at right angles to the 
direction of the wire conductor, but will take an oblique 
position. The directive forces of the earth's magnetism 
are tending to makq. the needle point north-and-south. 
The electric current is acting on the needle, tending 
to make it set itself west-and-east. The resultant 
force will be in an oblique direction between these, 
and will depend upon the relative strength of the two 
conflicting forces. If the current is very strong the 
needle will turn widely round ; but could only turn com- 
pletely to a right angle if the current were infinitely 
strong. If, however, the current is feeble in comparison 
with the directive magnetic force, the needle will turn 
very little. 

This arrangement will, therefore, serve roughly as a 
Galvanoscope or indicator of currents ; for the move- 
ment of the needle shows the direction of the current, 
and indicates whether it is a strong or a weak one. 
This apparatus is too rough to detect very delicate cur- 
rents. To obtain a more sensitive instrument there are 
two possible courses: (i.) increase the effective action 
of the current by carrying the wire more than once 
round the needle; (ii.) decrease the opposing dkective 
force of the earth's magnetism by some compensating 
contrivance. 

200. Schweigger's Multiplier. — The first of the 
above suggestions was carried out by Schw^eigger, who 
constructed a muliipUer of many turns of wire. A suit- 
able frame of wood, brass, or ebonite, is prepared to 
receive the wire, which must be " insulated," or covered 
with silk, or cotton, or guttapercha, to prevent the 
separate turns of the coil from coming into contact with 
each other. Within this frame, which may be circular, 
elliptical, or more usually rectangular, as in Fig. 110, the 
needle is suspended, the frame being placed so that 
the wires lie in the magnetic meridian. The greater the 
number of tarns the more powerful will be the magnetic 



CHAP. Ill 



ASTATIC COMBIXATIOXS 



185 




him 



Fig. 110. 

ve the term Gal- 



deflexion produced by the passage of equal quantities of 
current. But if the wire is thin, or tlie number of turns 
of wii'e numerous, the 
resistance thereby offered 
to the flow of electricity 
may very greatly reduce 
the strength of the current. 
The student will grasp the 
importance of this observa- 
tion when he has read the 
chapter on Ohm's Law. 
Gumming, of Cambridge, 
appears to have been the 
first to use a coil surround- 
ing a pivoted needle to 
measure the current. To 
vanometer. 

201. Astatic Combinations. — The directive force ex- 
ercised by the earth's magnetism on a magnetic needle 
may be reduced or obviated by one of two methods : — 

(a) \_Hauy's Metliod']. By employing a compensating 
magnet. An ordinary long bar magnet laid in the mag- 
netic meridian, but with its IS^-seeking pole directed 
towards the north, will, if placed horizontally above or 
below a suspended magnetic needle, tend to make the 
needle set itself with its S-seeking pole northwards. If 
near the needle it may overpower the directive force of 
the earth, and cause the needle to reverse its usual posi- 
tion. If it is far away, all it can do is to lessen the 
directive force of the earth. At a certain distance the 
m.agnet will just compensate this force, and the needle 
will be neutral. This arrangement for reducing the 
earth's directive force is applied in the reflecting galva- 
nometer shown in Fig. 122, in which the magnet at the 
top, curved in form and capable of adjustment to any 
height, affords a means of adj Listing the instrument to the 
desired degree of sensitiveness by raising or lowering it. 



186 



ELECTRICITY AKD MAGNETISM part i 




(b) [Nobiirs Method']. By using an astatic pair of 
magnetic needles. If two magnetized needles of equal 
strength and size are bound together by a light wire of 
brass, or aluminium, in re- 
versed positions, as shown 
in Fig. Ill, the force urging 
one to set itself in the mag- 
netic meridian is exactly 
counterbalanced by the force 
that acts on the other. Con- 
sequently this pak of needles 
will remain in any position 
in which it is set, and is 
independent of the earth's 
magnetism. Such a com- 
bination is known as an astatic pair. It is, however, 
difficult in practice to obtain a perfectly astatic pair, 
since it is not easy to magnetize two needles exactly 
to equal strength, nor is it easy to fix 
them perfectly parallel to one another. 
Such an astatic pair is, however, readily 
deflected by a current flowing in a wire 
coiled around one of the needles ; for, 
as shown in Fig. 112, the current 
which flows above one needle and 
below the other will urge both in the 
same direction,because they are akeady 
in reversed positions. It is even pos- 
sible to go further, and to carry the 
wu-e round both needles, winding the coil aromid the 
upper in the opposite sense to that in which the coil is 
wound round the lower needle. Several other astatic 
combinations are possible. For example, two needles 
may be set vertically, with similar poles upward, at the 
ends of a pivoted horizontal strip of wood or brass. 

Xobili applied the astatic arrangement of needles to 



,y^ 




the multiplying coils of Schweigger, and thus constructed 



\ * / 



CHAP. Ill MAGNETIC WHIRLS 187 

a very sensitive instrument, the Astatic Galvanovieter, 
shoTVQ in Fig. 119. The special forms of galvanometer 
adapted for the measurement of currents are described 
in the next lesson. 

202. Magnetic Field due to Current: Magnetic 
Whirls. — Arago found that if a current be passed 
through a piece of copper wire it becomes capable of 
attracting iron filings to it so long as the current flows. 
These filings set themselves at right angles to the wire, 
and cling around it, but drop off when the circuit is 
broken. There is, then, a magnetic "field," around the 
wire which carries the 
current; and it is im- <^ 
portant to know how the ^ \^ 

lines of force are dis- 
tributed in this field. 

Let the central spot in " 
Fig. 113 represent an im- ■^^°" ^^^' 
aginary cross-section of the wire, and let us suppose the 
current to be flowing in through the paper at that point. 
Then by Ampere's rule a magnet needle placed below will 
tend to set itself in the position shown, with its N" pole 
pointing to the left.* The current will urge a needle 
above the wire into the reverse position. A needle on 
the right of the current will set itself at right angles to 
the current {i.e. in the plane of the paper), and with its 
N pole pointing down, while the IS" pole of a needle on 
the left would be urged up. In fact the tendency would 
be to urge the I*^ pole round the conductor in the same 



* If the student has any difficultj^ in appljang Ampere's rule to this 
case and the others which succeed, he should carefully follow out the fol- 
lowing mental operation. Consider the spot marked "iw" as a hole in 
the ground into which the current is 'flowing, and into which he dives 
head-foremost. While in the hole he must turn round so as to face each 
of the magnets in succession, and remember that in each case the N- 
seeking pole ^^ill be urged to Ms left. In diagram 84 he must conceive 
himself as coming up out of the hole in the groupd where the current is 
flowing out. 



i 




188 



ELECTRICITY AND MAGNETISM part i 



way as the hands of a watch move; while the S pole 
would be urged in the opposite cyclic direction to that of 
the hands of a watch. If the current is reversed, and is 
regarded as flowing towards the reader, i.e. coming up 
out of the plane of the paper, as in the diagram of Fig. 
114, then the motions would be just in the reverse sense. 
It would seem from this as if a !N'-seeking pole of a 
magnet ought to revolve continuously round and round a 
current ; but as we cannot obtaui a magnet with one 
pole only, and as the S-seeking pole is urged in an oppo- 
site direction, all that occurs is that the needle sets itself 
as a tangent to a circular cui've 
surrounding the conductor. The 
field surrounding the conductor 
consists in fact of a sort of en- 
veloping magnetic whirl all along 
it, the whirl being strong near 
the wire and weaker farther away. 
This is what Oersted meant when 
he described the electric current 
as acting " in a revolving manner " 
upon the magnetic needle. The 
field of force, with its circular lines surrounding a current 
flowing in a straight conductor, can be examined experi- 
mentally with iron filings in the following way : A card 
is placed horizontally and a stout copper wire is passed 
vertically through a hole in it (Fig. 115). Iron filings 
are sifted over the card (as described in Art. 119), and a 
strong current from three or four large cells is passed 
through the wire. On tapping the card gently the filings 
near the wire set themselves in concentric circles round it. 
It is because of this surrounding field that two con- 
ductors can apparently act on one another at a distance. 
If both currents are flowmg in the same direction, their 
magnetic fields tend to merge, and the resulting stress in 
the medium tends to drag them together with an appa- 
rent attraction. If the currents are flowing in opposite 




Fi?. 115. 



CHAP. Ill 



MAGNETIC SHELL 



189 



directions the stresses in the intervening magnetic field 
tend to thrust them apart (see also Art. 389). 

It is known that energy has to be spent in producing 
any magnetic field. AYhen a current is turned on in a 
wire the magnetic field grows around the wu-e, some of 
the energy of the battery being used during the growth 
of the current for that purpose. One reason why electric 
currents do not instantly rise to their final value is be- 
cause of the reactive effect of this surrounding magnetic 
field. Xo current can exist without this surrounding- 
magnetic field. Indeed it is impossible to refute the 
proposition that what we commonly call an electric 
current in a wire really is this external magnetic 
whirl. 

203. Equivalent Magnetic Shell : Ampere's Theorem. 
— For many purposes the following way of regarding 
the magnetic action of electric currents is more con- 
venient thau the preceding. Suppose we take a battery 
and connect its terminals by a circuit of wire, and that 




Fi-. 116. 



a portion of the circuit be twisted, as in Fig. 116, into 
a looped curve, it will be found that the entire space 
enclosed by the loop possesses magnetic properties. In 
our figure the current is supposed to be flowing round 



190 ELECTEICITY AND MAGNETISM part i 

the loop, as viewed from above, in the same direction as 
the hands of a clock move round; an imaginary man 
swimming round the circuit and always facing towards 
the centre would have his left side do'^ii. By Ampere's 
rule, then, a X pole would be m-ged downwards through 
the loop, while a S pole would be urged upwards. In 
fact the space enclosed by the loop of the circuit behaves 
like a magnetic shell (see Art. 118), having its upper face 
of S-seeking magnetism, and its lower face of X-seeking 
magnetism. It can be shoT^m in every case that a closed 
voltaic circuit is equivalent to a magnetic shell whose edges 
coincide in j^osition icith the circuit, the shell being of 
such a strength that the number of its lines of force 
is the same as that of the lines of force due to the 
current in the circuit. The circuit acts on a magnet 
attracting or repelling it, and being attracted or repelled 
by it, just exactly as its equivalent magnetic shell would 
do. Also, the circuit itself, when placed in a magnetic 
field, experiences the same force as its equivalent mag- 
netic shell would do. 

204. Maxwell's Rule. — Professor Clerk Maxwell, 
who developed this method of treating the subject, has 
given the following elegant rule for determining the 
mutual action of a circuit and a magnet placed near it. 
Every jjortion of the circuit is acted upon hy a force urging 
it in such a direction as to make it enclose within its embrace 
the greatest possible number of lines of force. If the cir- 
cuit is fixed and the magnet movable, then the force 
acting on the magnet will also be such as to tend to 
make the number of lines of force that pass through 
the circuit a maximum (see also Art. 319). 

This is but one case of the still more general law 
governing every part of every electromagnetic system, 
viz. : Every electromagnetic system tends so to change the 
configuration of its p>arts as to make the flux of magnetic 
lines through the exciting circuit a maximum. (Art. 379.) 

205. De la Rive's Floating Battery. — The preced 



CHAP. Ill 



FLOATIXG BATTERY 



191 



ing remarks may be illustrated experimentally by the 
aid of a little floating battery. A plate of zinc and one 
of cop23er (see Fig. 117) are fixed side by side in a large 
cock, and connected above by a coil of several windings of 
covered copper wire. This is floated upon a dish contain- 
ing dilute sulphuric acid. If one pole of a bar magnet 
be held towards the ring it will be attracted or repelled 
according to the pole employed. The floating circuit will 
so move as to make the flux of magnetic lines through the 




Fig. 117. 

coil a maximum. If the S pole of the magnet be pre- 
sented to that face of the ring which acts as a S-seeking 
pole (viz. that face round which the current is flowing in 
a clockwise direction), it will repel it. If the pole be 
thrust right into the ring, and then held still, the battery 
will be strongly repelled, will draw itself off, float away, 
turn round so as to present toward the S pole of the 
magnet its N-seeking face, will then be attracted up, and 
will thread itself on to the magnet up to the middle, in 



192 ELECTRICITY AND MAGNETISM part i 

which position as many magiietic lines of force as pos- 
sible cross the area of the ring. 

It can be shown also that two cii'cuits traversed by 
currents attract and repel one another just as two mag- 
netic shells would do. 

It will be explained in Lesson XXXI. on Electromag- 
nets how a piece of iron or steel can be magnetized by 
causing a current to flow in a spiral wire round it. 

206. Strength of the Current in Magnetic Measure. 
— AVhen a current thus acts on a magnet pole near 
it, the force / which it exerts will be proportional to 
the strength C of the cm-rent, and proportional also to 
the strength m of the magnet pole, and to the length I 
of the wii'e employed : the force exerted between each ele- 
ment of the circuit and the pole will also vary inversely as 
the square of the distance r between them. If the wire 
is looped into a circular coil with the magnet pole at the 
centre, so that each portion of the circuit is approximately 

at the same distance from the pole. / = —^ dynes. 

Suppose the wire looped up into a circle round the magnet 

27rC 

pole, then I = '2TTr, and / = m dynes. Suppose also 

that the circle is of one centimetre radius, and that the 

magnet pole is of strength of one unit (see Art. 352), 

then the force exerted by the current of strength C 

•^ttC 
will be ^^^—- X 1, or 27rC dynes. In order, therefore, that 

a current of strength C should exert a force of C dynes on 
the unit pole, one must consider the cm-rent as travelling 

round only ^^— part of the circle, or round a portion of 

the circumference equal in length to the radius. 

207. Unit of Current. — A current is said to have a 
strength of one '• absolute " unit when it is such that if one 
centimetre length of the circuit is bent into an arc of one 
centimetre radius, the current in it exerts a force of 



7P 



Fiff. 118. 



CHAP. Ill GALVANOMETERS 193 

one dyne on a magnet-pole of unit strength placed at the 
centre of the arc. The practical unit of " one ampere " is 
only ^ of this theoretical unit (see also 
Art. 354). 

If the wire, instead of being looped into a 
coil, is straight and of indefinite length, the 
force which the cm-rent in it exerts upon a 
pole of strength m placed at point P near 
it w^ill be found to vary inversely as the 
simple distance (not as the square), and the 
pole will tend to move at right angles both 
to the wire and to the line OP. In Fig. 118 
the descending current will (according to 
the corkscrew rule above) tend to drive a JST pole at P 
towards the spectator. If the current is C amperes the 
force (in d}Ties) on the pole of m units will (see Art. 313) be 

/=2mC/10r. 

Example. — The force exerted by a current of 60 amperes 
in a long straight conductor upon a pole of 200 units 
placed 2 centimetres away from it will be 1200 dynes, 
or (dividing by ^r = 981) about 1*22 grammes' weight. 



Lessox XYII. — Galvanometers 

208- The term Galvanometer is applied to an in- 
strument for measuring the strength of electric currents 
by means of their electromagnetic action. There are 
two general classes of Galvanometers : (1) those in which 
the current flowing in a fixed coil of wire causes the 
deflexion of a pivoted or suspended magnetic needle ; (2) 
those in which the current flowing in a movable coil 
suspended between the poles of a fixed magnet causes the 
coil to turn. There is a third kind of instrument (called 
for distinction electrodynamometer, see Art. 394), in w^hich 
both the moving part and the fixed part are coils. These 
last are used chiefly for alternating-currents. 



194 ELECTRICITY AND MAGNETISM part i 

The simple arrangement described in Art. 199 was 
termed a " Galvanoscope," or current indicator, but it 
could not rightly be termed a " galvanometer " * or current 
measurer, because its indications were only qualitative, not 
quantitative. The indications of the needle did not afford 
accurate knowledge as to the exact strength of current 
flowing through the instrument. A good galvanometer 
must fulfil the essential condition that its readings shall 
really measure the strength of the current in some cer- 
tain way. It should also be sufficiently sensitive for the 
cm-rents that are to be measured to affect it. The 
galvanometer adapted for measuring very small currents 
(say a current of only one or two millionth parts of an 
ampere') will not be suitable for measuring very strong 
currents, such as are used in electric lighting or electro- 
plating. Large currents need thick wires ; and a coil of few 
turns will suffice. If very small currents are to turn the 
needle they must circulate hundreds or thousands of times 
around it, and therefore a coil of many turns is appro- 
priate, and the wire may be a very fine one. Moreover, 
if the current to be measured has already passed through 
a circuit of great resistance (as, for example, some miles 
of telegraph wire), a galvanometer whose coil is a short 
one, consisting only of a few tmnis of wire, will be of no 
use, and a long-coil galvanometer must be emploj^ed with 
many hundreds or even thousands of turns of insulated 
wire round the needle. The reason of this is explained 
hereafter (Art. 408). Hence it wiU be seen that different 
styles of instrument are needed for different kinds of 
works ; but of all it is requu-ed that they should afford 
quantitative measurements, that they should be sufficiently 
sensitive for the current that is to be measured, and carry 
that current without overheating. 

* The terms liheoscope and Bheometer are still occasionally applied to 
these instruments. A current interrupter is sometimes called a JRheotome, 
and the Commutator or Current Eeverser, shown in Fig. 136, is in some 
books called a liheotrope ; but these terras are dropping out of use. 



CHAP. Ill METHODS OF USE 195 

209. Methods of Control. — In all instruments, 
whether the moyhig part be a magnet or a coil, some 
controlling force is needful, otherwise the very smallest 
current would turn the index completely about. If small 
currents are to produce a small deflexion, and larger cur- 
rents a larger, there must be forces tending to control. 
Several means of control may be used. These are : — 

(a) Earth's Magnetic Force. — When the needle is hung 
on pivot or fibre, the earth's magnetic force tries to bring 
it back into the magnetic meridian. This is the com- 
monest method in galvanometers with moving needles. 

(6) Torsion of Wire. — Moving part in turning twists 
the suspending wire, which then tries to untwist, with a 
force which increases as the angle of deflexion. This 
method is commonest in galvanometers with suspended 
coils. 

(c) Gravity. — If needle is pivoted on trunnions to move 
in vertical plane, it may be weighted at one end. 

(d) Permanent Magnet Control. — To render a needle 
instrument independent of position, it may be arranged 
with a powerful external steel magnet to bring the needle 
back to zero. 

(e) Bifilar Suspension. — A needle or coil hung by 
two parallel threads tends by gTavity to return to its 
initial position. 

To make an instrument very sensitive the control 
must be weakened as much as possible. 

210. Methods of Observation. — There are follow- 
ing methods of using galvanometers in making observa- 
tions : — 

(i.) Dejlexion Method. — The angle through which the 
moving part (whether needle or coil) is deflected 
is read off on a scale, by pointer or reflected beam 
of light, when the moving part has come to rest. 
This is the commonest method. 

(ii.) Torsion Method. — The moving part is suspended 
by a wire from a torsion head, which is turned 



196 ELECTRICITY AND MAGNETISM part i 

round until the index is brought back to zero ; 
the controlling force then balancing the deflect- 
ing force. This very accurate method, due to 
Ohm, is used in Siemens' electrodynamometer 
(Art. 394). 

(iii.) First Siving Method. — Instead of waiting for 
moving part to come to rest the first siving may 
be observed. This method which is the only 
one practicable for sudden discharges, or for 
transient currents, is called the ballistic method 
(see Art. 218). If the moving part is not 
damped in its motion the first swing on turn- 
ing on a battery current is exactly twice the 
angle at which the deflexion settles down. 

(iv.) Oscillation Method. — Instead of observing deflex- 
ion, the time of oscillation of the needle may 
be observed, the coil being in this method set 
at right angles to the magnetic meridian. Al- 
lowance must be made, as in Art. 133, for the 
earth's magnetism. 
(v.) Cumulative Method. — For very minute currents 
a method is sometimes adopted to get up a 
measurable swing by reversing the current (by 
hand) as the needle swings through zero. 
Sometimes a rotating commutator of special 
construction is employed to produce, and accu- 
mulate, the successive impulses. 

(vi.) Null Methods. — In many cases combinations are 
used (AVheatstone's " Bridge," " Differential 
Galvanometers," etc.) of such a kind that when 
the conditions of electrical equilibrium are at- 
tained no current will flow through the galva- 
nometer in the circuit. Such methods, which 
are generally exceedingly accurate, are known 
as null methods. For such methods sensitive 
galvanometers are applicable, but the gradua- 
tion of their scale is unimportant. 



CHAP. Ill 



ASTATIC GALVANOMETER 



197 



211. Nobili's Astatic Galvanometer. — The instru- 
ment constructed by Xobili, consisting of an astatic pair 
of needles delicately hung, so that the lower one lay 
within a coil of wire wound upon an ivory frame (Fig. 
119), was for long the favourite form of sensitive gal- 
vanometer. The needles of this instrument, being inde- 
pendent of the earth's magnetism, take their position in 
obedience to the torsion of the fibre by which they are 
hung. The frame on which the coil is wound must be 
set carefully parallel to the needles ; and three screw feet 
serve to adjust the 



base of the instru- 
ment level. Protec- 
tion against currents 
of air is afforded by a 
glass shade. When 
a current is sent 
through the wii'e coils 
the needles move to 
right or left over 
a graduated circle. 
When the deflexions 
are small (i.e. less than 
10° or 15°) they are 
very nearly propor- 
tional to the strength 
of the currents that 




Fig. 119. 



produce them. Thus, if a current produces a deflexion 
of 6° it is known to be approximately three times as 
strong as a current which only turns the needle through 
2°. But this ai3proximate proportion ceases to be true 
if the deflexion is more than 15° or 20° ; for then the 
needle is not acted upon so advantageously by the cur- 
rent, since the poles are no longer within the coils, but 
are protruding at the side, and, moreover, the needle 
being oblique to the force acting on it, part only of the 
force is turning it against the directive force of the fibre ; 



198 



ELECTRICITY AND MAGNETISM part i 



the other part of the force is uselessly puEmg or pushmg 
the needle along its length. It is, however, possible to 
calibrate the galvanometer — that is, to ascertain by 
special measarements, or by comj^arison with a standard 
instrument, to what strengths of cm-rent particular 
amounts of deflexion correspond. Thus, suppose it once 
known that a deflesion of 32° on a particular galva- 
nometer is produced by a current of j^q of an ampere, 
then a current of that strength will always produce on 
that instrument the same deflexion, unless from any 
accident the controlling force has been altered. 

212. The Tangent Galvanometer. — It is not — for 
the reasons mentioned above — possible to construct a 




Fipr. 120. 



galvanometer in which the angle (as measured in degrees of 
arc) through which the needle is deflected is proportional 
throughout its whole range to the strength of the current. 
But it is possible to construct a very simple galvanometer 



CHAP. Ill TAXGENT GALVANOMETER 199 

in which the tangent* of the angle of deflexion shall be 
accurately proportional to the strength of the current. 
The essential feature of all tangent galvanometers is that 
while the coil is a large open rmg the needle is relatively 
very small. Fig. 120 shows a form of Tangent Galva- 
nometer suitable for large currents. The coil of this in- 
strument consists of a simple circle of stout copper wire 
from 10 to 15 inches in diameter. Other tangent gal- 
vanometers have many turns of fine wire wound upon 
a large open ring. At the centre is delicately suspended 
a magnetized steel needle not exceeding 1 inch in length, 
and usually furnished with a light index of aluminium. 
The instrument is adjusted by setting the coil in the 
magnetic meridian, the small needle lying then in the 
plane of the coil. 

The " field " due to a current passing round the circle 
is very uniform at and near the centre, and the lines of 
force are there truly normal to the plane of the coil. 
This is not true of other parts of the space inside the 
ring, the force being neither uniform nor normal in direc- 
tion, except centrally in the plane of the coil and along 
the axis. The needle being small, its poles are never 
far from the centre, and hence never protrude into the 
regions where the field is irregular, f Whatever mag- 
netic force the current in the coil can exert on the needle 
is exerted normally to the plane of the ring, and there- 
fore at right angles to the magnetic meridian. As the 
two forces — that due to the current and that due to the 
controlling magnetism of the earth — act squarely to one 



* See note on Ways of Reckoning Angles, p. 133. 

t In order to ensure uniformity of field, Gaugain proposed to hang the 
needle at a point on the axis of the coil distant from its centre by a distance 
equal to half the radius of the coils. Helmholtz's arrangement of two 
parallel coils, symmetrically set on either side of the needle, is better ; and 
a three-coil galvanometer, having the central coil larger than the others, so 
that all three may lie in the surface of a sphere having the small needle at 
its centre, is the best arrangement of all for ensuring that the field at the 
centre is uniform. 



200 



ELECTRICITY AND MAGNETISM part i 



another, the action of the current will not be measured 
by equal degrees marked out around a circle, but will be 
measured by equal divisions along a tangent line, as 
shown below. 'Now, it was proved in Art. 137 that 
the magnetic force which, acting at right angles to the 
meridian, produces on a magnetic needle the deflexion 5 
is equal to the horizontal force of the earth's magnetism 
at that place multiplied by the tangent of the angle of 
deflexion. Hence a current flowing in the coil will turn 
the needle aside through an angle such that the tangent of 
the angle of deflexion is proportional to the strength of the 
current. 

^a;amp?e.— Suppose a certain battery gave a deflexion of 
15° on a tangent galvanometer, and another battery 
yielding a stronger current gave a deflexion of 30°. The 
strengths currents are 7iot in the proportion of 15 : 30, 
but in the proportion of tan 15° to tan 30°. These 
values must be obtained from a table of natural tan- 
gents like that given in Appendix A, from which it will 
be seen that the ratio between the strengths of the cur- 
rents is -268: -577, or about 10: 22. 

Or, more generally, if current C produces deflexion S, and 
current C deflexion 6', then 



C:C 



tan 5 : tan 



To obviate reference to a table of figures, the circular 
scale of the instrument is sometimes graduated into 



c 


) 


5 


10 

J 1 J J 


15 


20 

, . J . ■ 


25 


30 " 


/"" 


/ 


^ 


p 




'l^^ 


^^ 




( C 


/ . 


'<0^ 


1 











Fi?. 121. 



tangent values instead of being divided into equal 
degrees of arc. Let a tangent OT be drawn to the 



CHAP. Ill TANGENT SCALES 201 

circle, as in Fig. 121, and along this line let any nam- 
ber of equal divisions be set off, beginning at O. From 
these points draw back to the centre. The circle will 
thus be divided into a number of pieces, of which those 
near O are nearly equal, but which get smaller and 
smaller away from O. These unequal pieces correspond 
to equal increments of the tangent. If the scale were 
divided thus, the readings would be proportional to the 
tangents. It is, however, harder to divide an arc into 
tangent lines with accuracy than to divide it into equal 
degrees ; hence this graduation, though convenient, is not 
used where great accuracy is needed. 

213. Absolute Measure of Current by Tangent Gal- 
vanometer. — The strength of a current may be deter- 
mined in " absolute " units by the aid of the tangent 
galvanometer if the " constants " of the instrument are 
known. The tangent of the angle of deflexion repre- 
sents (see Art. 137) the ratio between the magnetic force 
due to the current and the horizontal component of the 
earth's magnetic force. Both these forces act on the 
needle, and depend equally upon the magnetic moment 
of the needle, which, therefore, we need not know for 
this pm-pose. We know that the force exerted by the 
current at centre of the coil is proportional to the 
horizontal force of the earth's magnetism multiplied 
by the tangent of the angle of deflexion. These two 
quantities can be found from the tables, and from them 
we calculate the absolute value of the current as fol- 
lows : — Let r represent the radius of the galvanometer 
coil (measured in centimetres) ; its total length (if of one 
turn only) is 2 irr. The distance from the centre to all 
parts of the coil is of course r. From our definition 
of the unit of strength of current (Art. 207), it follows 

that C X ■^^^ = force (in dynes) at centre, 



or 



C x^ = H-tan8; 



202 ELECTRICITY AND MAGNETISM part i 



hence C = — • H • tan 8. 

27r 

The quantity 2 7r/r, or 2 7rn/r if the coil has n turns, 
is sometimes called the " constant " or the " principal 
constant " of the galvanometer and denoted by the sym- 
bol G. Hence the value of the current in absolute 
(electromagnetic) units * will be expressed as 

C = — . tan 8. 
G 

The constant G represents the strength of field pro- 
duced at the centre of the coil by unit current. 

214. Sine Galvanometer. — The disadvantage of 
the tangent galvanometer Just described is that it is not 
very sensitive, because the coil is necessarily very large 
as compared with the needle, and therefore far away 
from it. A galvanometer with a smaller coil or a larger 
needle could not be used as a tangent galvanometer, 
though it would be more sensitive. Any sensitive 
galvanometer in which the needle is directed by the 
earth's magnetism can, however, be used as a Sine 
Galvanometer, provided the frame on which the coils 
are wound is capable of being turned round a central 
axis. When the instrument is so constructed, the fol- 
lowing method of measuring currents is adopted. The 
coils are first set parallel to the needle (i.e. in the mag- 
netic meridian) ; the current is then sent through it, 
producing a deflexion ; the coil itself is rotated round 
in the same sense, and, if turned round through a wide 
enough angle, w^ill overtake the needle, wiiicli will once 
more lie parallel to the coil. In this position two forces 
are acting on the needle : the directive force of the earth's 
magnetism acting along the magnetic meridian, and the 
force due to the cm-rent passing in the coil, which tends 
to thrust the poles of the needle out at right angles ; 

* The student will remember (Arts. 207 and 354) that the practical unit 
of current which we call " one ampere " is only ^^^ of one " absolute " unit 
of the centimetre-gramme-second sj-stem. 



CHAP. Ill MIRROR GALYAXOMETER 203 

in fact there is a " couple " which exactly balances the 
" couple " due to terrestrial magnetism. Now it was 
shown in the Lesson on the Laws of Magnetic Force 
(Art. 136) that when a needle is deflected the " moment " 
of the couple is proportional to the sine of the angle of 
deflexion. Hence in the sine galvanometer, when the 
coil has been turned round so that the needle once more 
lies along it, the stretigth of the current in the coil is pro- 
portional to the sine of the angle through ivhich the coil has 
been turned.* 

215. The Mirror Galvanometer. — When a galva- 
nometer of great delicacy is needed, the moving parts 
must be made very light and small. To watch the move- 
ments of a very small needle an mr/ex of some kind must 
be used ; indeed, in the tangent galvanometer it is usual to 
fasten to the short stout needle a delicate stiff pointer of 
aluminium. A far better method is to fasten to the 
needle a very light muTor of silvered glass, by means of 
which a beam of light can be reflected on to a scale, so 
that every slightest motion of the needle is magnified 
and made apparent. The mirror galvanometers devised by 
Sir W. Thomson (Lord Kelvin) for signalling through 
submarine cables, are admirable examples of this class of 
instrument. In Fig. 122 the general arrangements of this 
instrument are shown. The body of the galvanometer, 
consisting of a bobbin on which is wound the coil, is sup- 



* Again the student who desires to compare the strength of two cur- 
rents will require the help of a table of natural sines, like that given in 
Appendix A. Suppose that with current C the coils had to be turned 
through an angle of degrees; and that with a different current C the 
coils had to be turned through 9' degrees, then 

C :C' = sin e : sin 6'. 

It is of course 'assumed that the instrument is provided Avith a scale of 
degrees on which to read off the angle through which the coils have been 
turned. It is possible here also, for rough purposes, to graduate the circle 
not in degrees of arc, but in portions corresponding to equal additional 
values of the sine. The student should try this way of dividing a circle 
after reading the note On Ways of Reckoning Angles, p. 133. 



204 



ELECTRICITY AND MAGNETISM part 



ported on three screw feet by which it can be adjusted. 
The magnet consists of one or more small pieces of steel 
watch-spring attached to the back of a light concave sil- 
vered glass mirror about as large as a threepenny piece, 
weighing altogether only two or three gTains. This mii'- 
ror is hung by a single fibre of cocoon silk within the 
coil, and a curved magnet, which serves to counteract the 




Fig. Hi. 



magnetism of the earth, or to direct the needle, is carried 
upon a vertical support above. Another view of the sus- 
pended mirror and magnets is shown in Fig. 123. Oppo- 
site the galvanometer is placed the scale. A beam of 
light from a paraffin lamp passes through a narrow aper- 
ture under the scale and falls on the mirror, which reflects 
it back on to the scale. The mirror is slightly concave, 
and gives a well-defined spot of light if the scale is 
adjusted to suit the focus of the mirror. The adjusting 
magnet enables the operator to bring the reflected spot of 



CHAP. HI SENSITIVE GALVANOMETERS 



205 



light to the zero pomt at the middle of the scale. The 
feeblest current passing through the galvanometer will 
cause the spot of light to shift to right or left. The tiny- 
current generated by dipping into a drop of salt water 
the tip of a brass pin and a steel needle (connected by 
wii-es to the terminals of the galvanometer) will send the 
spot of light swinging right across the scale. If a pow- 
erful limelight is used, the movement of the needle can 
be shown to a thousand persons at once. For still more 
delicate work an astatic pair of needles can be used, each 





Tig. 123. 



Fig. 124. 



being surrounded by its coil, and having the mirror rig- 
idly attached to one of the needles. Such a form, with 
two bobbins, wound so as to be traversed by the current 
in opposite senses, is represented diagrammatically in Fig. 
124. Such an instrument, made with four bobbins, two 
in front and two behind the suspended needle system, and 
having on each bobbin about 2 miles of a wire about 
yoLq inch in thickness, insulated by a coating of silk, is 
capable of showing by a deflexion of one division on its 
scale an excessively minute current, even down to one 
fifty-four thousand millionth part of one ampere. 

216. Suspended Coil Galvanometers. — These have 
been used by Sturgeon (1836), Varley (1860), and others, 
and the principle was also applied in Lord Kelvin's 



206 



ELECTRICITY AND MAGNETISM part 




Fig. 125. 



" Siphon Recorder." The best known is that of D'Arson- 

val depicted in Fig. 125. Between the poles of a 
compound permanent steel magnet of 
U-shape is suspended by very thin 
hard-di-awn silver wires an open coil of 
very fine wire wound on a light rec- 
tangular frame. The current is led to 
and from the coil by the suspending 
wires. Within the suspended coil is a 
cylinder of soft ii'on, supported from 
behind, to concentrate the magnetic 
field. The vertical parts of the coil 
then hang freely in the two narrow 
gaps where the magnetic field is very 
intense. The force tending to tiu'n the 
coil is proportional to the current, to 
the number of windings, and to the 

intensity of the magnetic field, so that by making the 

magnet ver}^ powerful the instrument 

becomes very sensitive. The elasticity 

of the suspending wires controls the 

position of the coil and tends to bring 

it back to its initial position. These 

galvanometers are independent of the 

earth's magnetic field, and are not 

affected by magnets in their neigh- 
bourhood, so that they can be used 

in many places where other galva- 
nometers could not. They are also 

remarkably dead-beat. Some are 

provided with a pointer and a 

horizontal dial ; others more usually 

have a mirror attached to the coil 

to reflect a spot of light. 

Most recent is the suspended-coil 

galvanometer of Ayrton and Mather (Fig. 126). Here the 

suspended coil is formed as an elongated loop with no 




Fig. 126. 



CHAP. Ill SPECIAL GALVANOMETERS 207 

aperture between its sides. Consequently the poles of 
the magnets may he brought very close together; and 
these are made up of a number of flat steel magnets of 
nearly cu-cular form piled up on one another. One of 
these instruments, with mirror and scale, will show a 
deflexion of one scale division, with a current less than 
one ninety-millionth part of 1 ampere. 

Strong ciuTents must not be passed through very sen- 
sitive galvanometers, for, even if they are not spoiled, the 
deflexions of the needle will be too large to give accurate 
measurements. In such cases the galvanometer is used 
with a shunt, or coil of wu'e arranged so that the greater 
part of the current shall flow through it, and pass the gal- 
vanometer by, only a small portion of the current actually 
traversing the coils of the instrument. The resistance 
of the shunt must bear a known ratio to the resistance of 
the instrument, according to the principle laid down in 
Art. 409 about branched circuits. 

217- Differential Galvanometer. — For the purpose 
of comparing two currents a galvanometer is sometimes 
employed, in which the coil consists of two separate wires 
wound side by side. If two equal currents are sent in 
opposite du^ections through these wires, the needle will 
not move. If the currents are, however, unequal, then 
the needle will be moved by the stronger of them, with 
an intensity corresponding to the difference of the 
strengths of the two currents. 

218. Ballistic Galvanometer. — In order to measure 
the strength of currents which last only a very short time, 
galvanometers are employed in which the needle takes a 
relatively long time to swing. This is the case with long 
or heavy needles ; or the needles may be weighted by 
enclosing them in leaden cases. As the needle swings 
slowly round, it adds up, as it were, the varying impulses 
received during the passage of a transient current. The 
sine of half the angle of the first swing is proportional to the 
quantity of electricity that has flowed through the coil. The 



208 ELECTRICITY AND MAGNETIS:M part i 

charge of a condenser may thus be measured by discharg- 
ing it through a ballistic galvanometer (see Art. 4186). 
The needle must not be damped. 

219. Methods of Damping: Aperiodic Galvano- 
meters. — To prevent the needle from swinging to and 
fro for a long time devices are used to damp the motion. 
These are : — 

(a) Air Damping. — A light vane attached to needle 
beats against the air and damps the motion. In mirror 
instruments the mirror itseK damps, particularly if con- 
fined in a narrow chamber. 

(6) Oil Damping. — A vane dips into oil. 

(c) Magnetic Damping. — If the needle swings close 
to or inside a mass of copper, it will soon come to rest by 
reason of the eddy-cmTents (Art. 457) induced in the 
copper. Eddy-currents damp the motion of the suspended 
coil in instruments of that class. 

The period of swing can be reduced by diminishing 
the weight and leverage of the moving parts so as to 
lessen their moment of inertia. It can also be lessened 
(at the expense of the sensitiveness of the instrument) 
by increasing the controlling forces. An instrument so 
well damped as to come to rest without getting up a 
periodic swing is called an aperiodic or dead-beat instru- 
ment. 

120. Voltmeters, or Potential Galvanometers. — If any 
galvanometer be constructed with a very long thin wire 
of high resistance as its coil, very little current will flow 
through it, but w^hat little current flows will be exactly 
proportional to the potential difference that may be 
applied to the two ends of its circuit. Such a galvano- 
meter, suitably provided with a scale, will indicate the 
number of volts between its terminals. Many forms of 
voltmeter-galvanometers exist, but they all agree in the 
essential of having a coil of a high resistance — sometimes 
several thousand ohms. The suspended-coil galvano- 
meters described in Art. 216 make excellent voltmeters. 



CHAP. Ill 



AMPEREMETERS 



209 



"Weston's voltmeter, largely used in America, is of this 
class, the coil being delicately pivoted, and controlled by 
a spiral spring. Any sensitive mirror galvanometer can 
be used as a voltmeter by simply adding externally to its 
circuit a resistance sufficiently great. There are also 
other voltmeters that depend on electrostatic actions; 
they are a species of electrometer and are described in Art. 
290. Cardew's voltmeter (see Art. 430) differs from the 
above class of instrument, and consists of a long thin 
platinum wire of high resistance, which expands by heat- 
ing when it is connected across a circuit. All voltmeters 
are placed as shunts across between the two points the 
potential difference of which is to be measured. They 
are never joined up hi circuit as amperemeters are. 

221. Amperemeters, or Ammeters. — A galvanometer 
graduated so that its index reads directly on the scale 
the number of amperes (Art. 207) 
flowing through the coil is called an 
Amperemeter. Such instruments were 
introduced in form for industrial use 
in 1879 by Ayrton and Perry. Many 
other forms were subsequently in- 
vented. In Ayrton and Perry's in- 
struments (Fig. 127), which are 
portable and " dead-beat " in action, 
the needle, which is oval in shape, is 
placed between the poles of a power- 
ful permanent magnet to control its 
direction and make it independent 
of the earth's magnetism. By a peculiar shaping of the 
pole-pieces, needle, and coils, the angular deflexions are 
proportional to the strength of the deflecting current. 
These amperemeters are made with short coils of very 
low resistance and few turns of wire. Ayrton and Perry 
also arranged voltmeters (Art. 220) in a similar form, but 
with long coils of high resistance. 

Among the innumerable forms of amperemeter in 





210 ELECTEICITY AND MAGXETIS.AI part i 

commerce there are a number in Avliicli there is neither 
magnet nor iron, but which depend upon the mutual 
force between a fixed and a movable coil traversed by 
the cm'rent. These are dealt with in 
Art. 394, and are suitable for alternate 
currents as well as contiauous currents. 
Of this kind are Siemens' electrodyna- 
mometer and the Kelvin balances. 

Other instruments depend upon the 
magnetic properties of iron under the 
influence of the current. Of this class 
are the Schuckert instruments repre- 
sented in Fig. 128. An index pivoted 
in the axis of an open coil carries a light strip of soft 
iron seen endways at B. Another strip A is fixed within 
the coil. The current flowing round the coil magnetizes 
these strips and they repel one another. Gravity is here 
the controlling force. 

Lessox X'ST^n. — Currents jyroduced by Induction 

222. Faraday's Discovery. — In 1831 Faraday dis- 
covered that currents can be induced in a closed circuit 
by moving magnets near it, or by moving the circuit 
across the magnetic field: and he followed up this dis- 
covery by finding that a current wliose strength is chang- 
ing may induce a secondary cm-rent in a closed circuit 
near it. Such currents, whether generated by magnets 
or by other currents, are known as Induction Currents. 
And the action of a magnet or current in producmg 
such induced currents is termed electromagnetic (or 
magneto-electric) induction,* or simply induction. Upon 

* The student must not confuse this electromagnetic induction with 
the phenomenon of the electrostatic induction of one charge of electricity 
by another charge, as explained in Lesson III., and which has nothing to 
do %vith currents. Formerly, before the identity of the electricity derived 
from different som-ces was understood (Art. 246), electricity derived thus 



ciLvp. Ill MAGNETO-ELECTRIC INDUCTION 



211 



this principle are based the modern dynamo machines 
for generating electric currents mechanically, as well as 
induction coils, alternate-current transformers, and other 
appliances. 

223. Induction of Currents by Magnets. — If a coil 
of insulated wire be connected in circuit with a suffi- 
ciently delicate galvanometer, and a magnet be inserted 
rapidly into the hollow of the coil (as in Fig. 129), a 
momentary current is observed 
to flow round the circuit while 
the magnet is being moved 
into the coil. So long as the 
magnet lies motionless in the 
coil it induces no currents. 
But if it be rapidly pulled out 
of the coil another momentary 
current will be observed to 
flow, and in the opposite 
direction to the former. The 
induced current caused by 
inserting the magnet is an 
inverse current, or is in the 
opposite direction to that 
which would magnetize the 
magnet with its existing polarity. The induced current 
caused by withdrawing the magnet is a direct current. 

Precisely the same effect is produced if the coil be 
moved towards the magnet as if the magnet were moved 
toward the coil. The more rapid the motion is, the 
stronger are the induced currents. 

The magnet does not grow any weaker by being so 
used, for the real source of the electrical energy generated 
is the mechanical energy spent in the motion. 

from the motion of magnets was termed magneto-electricity. For most 
purposes the adjectives magneto-electric and electro-magnetic are synony- 
mous. The production of electricity from magnetism, and of magnetism 
from electricity, are, it is true, two distinct operations ; but both are 
included in the branch of science denominated Electromagnetics. 




212 



ELECTRICITY AND MAGNETISM part i 



If the circuit is not closed, no currents are produced ; 
but the relative motion of coil and magnet will still set 
up electromotive-forces, tending to produce currents. 

Faraday discovered these effects to be connected with 
the magnetic field surrounding the magnet. He showed 
that no effect was produced unless the circuit cut across 
the invisible magnetic lines of the magnet. 

224. Induction of Currents by Currents. — Faraday 
also showed that the approach or recession of a current 
might induce a current in a closed circuit near it. This 
may be conveniently shown as an experiment by the 
apparatus of Fig. 130. 

A coil of insulated wire P is connected in circuit with 
a battery B of two or three cells, and a key K to tm'n the 




Fi^ 130 



current on or off. A second coil S, entirely unconnected 
with the first, is joined up with wires to a sensitive gal- 
vanometer G. We know (Art. 202) that a coil of wire 
in which a current is circulating acts like a magnet. 
And we find that if while the current is flowing in P, 
the coil is suddenly moved up toward S, a momentary 
current will be induced in S. If P is suddenly moved 
away from S another momentary current will be observed 
in the second circuit. The first of these two momentary 
currents is an " inverse " one, while the second one is 



CHAP. Ill INDUCTION OF CURRENTS 



213 



found to be a " direct " one (i.e. one which runs the same 
way round the coil S as the battery current runs round 
the coil P). The coil P is called the primary coil, and 
the current in it the primary current. The other coil S 
is called the secondary coil, and the momentary currents 
induced in it are sometimes called secondary currents. 

Let P now be placed close to S, no current flowing 
in either coil. Then on pressing the key K to turn on 
the primary current, it will be noticed that during the 
moment while the current in P is growing there will 
be a transient inverse current in S. The effect of turn- 
ing on the current is just as if the current had been 
turned on while P was far away and then P suddenly 
brought up to S. Breaking the battery circuit while the 
primary coil lies close to the secondary coil produces the 
same effect as if the primary coil were suddenly removed 
to an infinite distance. Making the battery circuit while 
the primary coil lies close to the secondary produces the 
same effect as bringing it up suddenly from a distance. 

So long as a steady current traverses the primary cir- 
cuit there are no induced currents in the secondary circuit, 
unless there is relative motion between the tw^o circuits ; 
but moving the secondary circuit towards the primary 
has just the same elfect as moving the primary circuit 
towards the secondary, and vice versa. 

We may tabulate these results as follows : — 



By 

means 
of 


Momentary Inverse 

currents are induced 

in the secondary circuit 


Momentary Direct 

currents are induced 

in the secondary circuit 


Magnet 


while approaching. 


while receding. 


Current 


while approaching, 

or beginning, 

or increasing in strength. 


while receding, 

or ending, 

or decreasing in strength. 



> . 



214 ELECTRICITY AND MAGNETISM part i 

225. Fundamental Laws of Induction. — When we 

reflect that every ch'cuit traversed by a current has a 

magnetic field of its own in which there are magnetic lines 

running through the cu'cuit (Arts. 202 and 389), we shall 

see that the facts tabulated in the preceding paragraph 

may be summed up in the following fundamental laws : — 

(i.) A decrease in the number of lines which pass through 

a circuit induces a current round the circuit hi 

the positive direction (i.e. produces a •' direct " 

current') ; ichile an increase in the number of lines 

which pass through the circuit iriduces a current 

in the negative direction round the circuit (i.e. an 

" inverse " current). 

Here we suppose the positive direction along lines to 

be the direction along which a free iN" pole would tend to 

move, and the positive direction of the current that 

which the current must flow to increase the magnetic 

flux. Compare the " corkscrew " rule given on p. 183. 

(ii.) The total induced electromotiveforce acting round 

a closed circuit is equal to the rate of decrease in 

the number of lines ivhich pass through the circuit. 

Suppose at first the number of magnetic lines (Art. 

119) passing through the circuit to be X^, and that after 

a very short interval of time t the number becomes Ng, 

the average induced electromotive-force E is 



By Ohm's law, C = E - R, 

therefore C ^^^~^' 



If ^2 is greater than X^, and there is an increase in the 
number of lines, then X^ — No wiUbe a negative quantity, 
and C will have a negative sign, showing that the E.M.F. 
is an inverse one. A coil of 50 turns of wke cutting 
1000 lines will produce the same effect as a coil of 5 



CHAP. Ill CUTTING MAGNETIC LINES 215 

turns cutting 10,000 lines, or of 1 turn cutting 50,000 
lines . 

To induce an electromotive-force equal to that of a 
single Daniell's cell would require that 110,000,000 lines 
should be cut in one second. As such large numbers 
are inconvenient to express the facts, the unit of E.M.F., 
the volt, has been chosen to correspond to the cutting of 
100,000,000 lines per second. 

Example. — Suppose the number of magnetic lines to dimin- 
ish from 800,000 to in the 5*0 of a second, the rate of 
diminution is 40,000,000 lines per second. And since 
1 volt is taken as lO^ lines per second, the average in- 
duced E.M.F. during that time will be 0-4 volt. 

A reference to Fig. 176 will make this important law 
clearer. Suppose ABCD to be a wire circuit of which the 
piece AB can slide along DA and CB towards S and T. 
Let the vertical arrows represent vertical lines of force in 
a uniform magnetic field, and show (as is the case with 
the vertical components of the earth's lines of force in the 
northern hemisphere) the direction in which a ]N'-pointing 
pole w^ould move if free. The positive direction of these 
magnetic lines is therefore vertically downwards through 
the circuit. Now if AB slide towards ST with a uniform 
velocity it will cut a certain number of lines every second, 
and a certain number will be added during every second 
of time to the total number passing through the circuit. 
If Nj be the number at the beginning, and Ng that at 
the end of a circuit, N^ — Ng will be a negative quantity, 
and there will be generated an electromotive-force whose 
direction through the sliding piece is from A towards B. 

It is important to note that all these inductive opera- 
tions are really magnetic. In the experiment with the 
two coils P and S it is the magnetic lines of coil P which 
pass through coil S and set up the induced E.M.F. This 
is proved by the following further experiment. Take a 
bar of iron — a poker, or better still, a bundle of iron 
wires — and lay it along the dotted line so that its ends 



216 



ELECTRICITY AXD MAGNETISM part i 



pass through P aud S. It Trill bv its gTeat magnetic per- 
meability help to conduct the mag-netic lines from P 
through S. And when it is so placed it will be found 
gTeatly to intensify the actions. In fact if P is many 
inches away fi'om S. and the iron core is present, the 
inductive effects of turning the current on and off may 
be as great as if. in the absence of the core, P were 
pushed up close to S. 

226. Direction of Induced E.M.F. — It is convenient 
to have rules for remembering the relations in direc- 
tion between the magnetism, the motion, and the in- 
duced electromotive -force. 
Of such rules the following, 
due to Fleming, is most use- 
ful : Let the forefinger of the 

.-^X right hand (Fig. ISl) point in 
the direction of the magnetic 
lines : then turn the thumb in 
the direction of the motion : the 
middle finger bent at right 
angles to both thumb and fore- 
finger will shore the direction of 
Fig. 131. the induced E.M.F. 

Another often given is an 
adaptation of Ampere's rule : Suppose a figure swiyjiming 
in any conductor to turn so as to look along the (positive 
direction of the) lines, then if he and the conductor be moved 
foivards his right hand he will be swimming icith the current 
induced by this motion; if he be moved towards his left 
hand, the cm-rent will be a^'aiust him. 

227. Faraday's Disk Machine. — Faraday constructed 
several magneto-electric machines, one of them consist- 
ing of a copper disk (Fig. 132) which he rotated between 
the poles of a steel magnet. The current flowed from 
shaft to rim or vice versa, according to the sense of 
the rotation. It was conducted away by wires having 
sliding contacts. In other machines copper wire coils 




CHAP. Ill 



FAKADAY'S APPARATUS 



217 



^TTb- 



were spun so as to cut magnetic lines. The same in- 
duction principle is applied in modern dynamo-electric 
machines (Lesson 
XLII.). In all cases 
power must be era- 
ployed to produce 
the motion. They 
are all contrivances 
for converting me- 
chanical energy into 
electrical energy. 

228. Faraday's 
Ring: Principle 
of Transformation. — 
Amongst Faraday's 
earliest experiments he took an iron ring about 8 inches 
in diameter (Fig. 133) and wound upon it two insulated 
coils of wire P and S, each of many turns. If coil P 
was connected to a battery circuit, and coil S to a 
galvanometer, he found that 




132. 



w^henever a current was 
turned on or off in coil 
P, secondary currents 
were generated in coil S. 
In fact the currents in 
P magnetized the iron 
ring, and the magnetic 
lines created by P passed 
through S, setting up 
induction currents. " If 
S is used as the primary 
then P will w^ork as secondary ; in fact the induction be- 
tween P and S is mutual. The Faraday ring, with its two 
coils wound upon a closed circuit of iron, maybe regarded 
as the very type of all transformers or induction coils. 
Faraday also employed some induction-coils in w^hich 
the two coils A and B (Fig. 134) were wound cylindri- 
cally outside one another upon a straight core C of iron. 





218 ELECTRICITY AND MAGNETISM part i 

In all transformers the electromotive-forces generated 
in the secondary circuit are to those employed in the 
primary circuit, nearly in the same 
proportion as the relative numbers of 
turns in the two coils. For example, 
if the primary coil has 100 turns and 
the secondary has 2500 turns, the 
electromotive-force in the secondary 
circuit will be nearly twenty-five 
times as great as that used in the 
primary. By choosing the proper 
number of turns, the electromotive-force can be trans- 
formed either up or down. 

229. The Induction Coil. — In order to generate 
enormously high electromotive-forces which shall be able 
to send sparks across air spaces that ordinary batteries 
working at under 100 volts coidd not possibly pierce, 
advantage is taken of the transformer principle. To pro- 
duce spark discharges there is used the apparatus depicted 
in Fig. 135, as improved by Callan, Sturgeon, Ruhmkorff, 
and others, and termed the Induction Coil or Inductorium. 
The induction coil consists of a cylindrical bobbin hav- 
ing a central iron core surrounded by a short inner or 
" primary " coil of stout wire, and by an outer " second- 
ary " coil consisting of many thousand turns of very fine 
wire, very carefully insulated between its different parts. 
The primary circuit is joined to the terminals of a few 
powerful Grove's or Bunsen's cells, and in it are also 
included an interrupter and a commutator or key. The 
object of the interrupter, is to make and break the 
primary circuit in rapid succession. The result of this 
is at every " make " to induce in the outer " secondary " 
circuit a momentary inverse current, and at every 
"break" a powerful momentary direct current. As 
the number of magnetic lines created and destroyed at 
each '^ make " and " break " is the same, the two electro- 
motive impulses are equal ; but by the use of a condenser 



CHAP, III 



INDUCTION COIL 



219 



the current at " make " is caused to take a considerable 
fraction of time to grow, whilst at " break " the cessation 
is instantaneous. The rate of cutting of the magnetic 
lines is therefore much gTeater at " break " than at 
" make." The induced electromotive-forces at " make " 
last longer, but are feebler, and do not suffice to send 
sparks. The currents at " break " manifest themselves 
as a brilliant torrent of sparks between the ends of the 




Fig. 135. 



secondary wires when brought near enough together. 
The primary coil is made of stout wire, that it may 
carry strong magnetizing currents, and consists of few 
turns to keep the resistance low, and to avoid self-induc- 
tion of the primary current on itself. The central iron 
core is for the purpose of increasing, by its great mag- 
netic permeability, the number of lines of force that pass 
through the coils : it is usually made of a bundle of fine 
wires to avoid the induced currents which if it were a 
solid bar would be set circulating in it, and which would 
retard its rapidity of magnetization or demagnetization. 



220 ELECTRICITY AXD MAGXETISM part i 



that the coefficient of transformation may be large ; and 
as the induced electromotive-force will be thousands of 
volts, the resistance of this coil will be immaterial, and it 
may be made of the thinnest wire that can conveniently 
be wound. In Mr. Spottiswoode's giant Induction Coil 
(which yields a spark of 42 i^ inches' length in air, when 
worked with 30 Grove's cells), the secondary coil contains 
280 miles of wire, wound in 340,000 turns, and has a 
resistance of over 100,000 ohms. 

The interrupters of induction coils are usually self- 
acting. That of Foucault, shown with the coil in Fig. 
135, consists of an arm of brass L, which dips a platinum 
wire into a cup of mercury ]\I, from which it draws the 
point out, so breaking circuit, in consequence of its other 
end being attracted toward the core of the coil whenever it 
is magnetized: the arm being drawn back again by a spring 
when, on the breaking of the ckcuit, the core ceases to be 
a magnet. A more common interrupter on small coils is 
a " break," consisting of a piece of thin steel which makes 
contact with a platinum point, and which is drawn back by 
the attraction of the core on the passing of a current ; and 
so makes and breaks circuit by A^brating backwards and 
forwards just as does the hammer of an ordinarv electric 
bell. 

Associated with the primary cu'cuit of a coil is usually 
a small condenser (see Art. 303). made of alternate layers 
of tuifoil and paraffined paper, into which the current 
flows whenever circuit is broken. The effect of the con- 
denser is, as stated above, to suppress the " inverse " 
current at "make" and to increase greatly the direct 
electromotive-force at " break." The sparks are longer, 
and only pass one way. The condenser does this by the 
action known as electric resonance (see Art. 517). 

230. RuhmkorfE's Reverser. — In order to cut off or 
reverse the direction of the battery current at will, 
Ruhmkorff applied the current-reverser, or reversmg- 



CHAP. Ill 



INDUCTION SPARKS 



221 



switch (" commutator ") shown in Fig. 136. In this 
instrument the battery poles are connected through the 
ends of the axis of a small ivory or ebonite cylinder to 
two cheeks of brass V and V, which can be turned so as 
to place them either way in contact with two vertical 
springs B and C, which are joined to the ends of the 
primary coil. Many other forms of re versing-s witch 
have been devised ; one, much used as a key for tele- 
gTaphic signalling, is drawn in Fig. 271. 




Fig. 136. 

231. Luminous Effects of Induction Sparks. — The 

induction coil furnishes a rapid succession of sparks 
with which all the effects of disruptive discharge may 
be studied. These sparks differ only in degree from 
those furnished by friction machines and by Leyden 
jars (see Lesson XXIV. on Phenomena of Discharge). 

For studying discharge through glass vessels and tubes 
from which the air has been partially exhausted, the coil 
is very useful. Fig. 137 illustrates one of the many 
beautiful effects which can be obtained, the spark ex- 
panding in the rarefied gas into flickering sheets of 
light, exhibiting striae and other phenomena. 



222 



ELECTRICITY AND MAGNETISM part i 



232. Induction Currents from Earth's Magnetism. — 

It is easy to obtain induced currents from the earth's 

magnetism. A coil of fine 
wire joined to a sensitive 
galvanometer, when sud- 
denly inverted, cuts the 
lines of the earth's magne- 
tism, and induces a current. 
Faraday, indeed, applied 
this method to investigate 
the direction and number of 
magnetic lines. If a small 
wire coil be joined in circuit 
with a suitable galvanometer 
having a heavy needle, and 
the little coil be suddenly 
inverted while in a magnetic 
field, it will cut twice all the 
lines that pass through its 
own area, and the sine of 
half the angle of the first 
swing (Art. 418) will be pro- 
portional to the number of 
lines cut; for with a slow- 
moving needle, the total 
quantity of electricity that 
flows through the coils will 
be the integral whole of all 
the separate quantities con- 
veyed by the induced cur- 
rents, strong or weak, which 
flow round the circuit during 
the rapid process of cutting the lines. The little exploring 
coil acts therefore as a magnetic proof-plane. For small 
deflexions the first swing may be taken as a sufficient 
approximation instead of the sine of half the angle (see 
Art. 418). 




Fig. 13i 



CHAP. Ill CHEMICAL DECOMPOSITION 223 

If the circuit be moved parallel to itself across a uni- 
form magnetic field there will be no induction currents, 
for just as many magnetic lines will be cut in moving- 
ahead in front as are left behind. There will be no cur- 
rent in a wire moved parallel to itself along a line of 
force ; nor, if it lie along such a line while a current is 
sent through it, will it experience any mechanical force. 

233. Earth Currents. — The variations of the earth's 
magnetism, mentioned in Lesson XII., alter the number 
of magnetic lines which pass through the telegraphic cir- 
cuits, and hence mduce in them disturbances which are 
known as " earth currents." During magnetic storms 
the earth currents on the British lines of telegraph have 
been known to attain a strength of 40 milliamperes, 
which is stronger than the usual working currents. 
Feeble earth currents are observed every day, and are 
more or less periodic in character. 

Lesson XIX. — Chemical Actiojis of Currents 

234. Conducting Properties of Liquids. — In addition 
to the chemical actions inside the cells of the battery, 
which always accompany the production of a current, 
there are also chemical actions produced outside the 
battery when the current is caused to pass through cer- 
tain liquids. Liquids may be divided into three classes 
— (1) those which do not conduct at cdl, such as turpentine 
and many oils, particularly petroleum; (2) those lohich 
conduct without decomposition, viz. mercury and other mol- 
ten metals, which conduct just as solid metals do ; (3) 
those which are decomposed when they conduct a current, 
viz. the dilute acids, solutions of metallic salts, and cer- 
tain fused solid compounds. 

235. Decomposition of Water. — In the year 1800 
Carlisle and Nicholson discovered that the voltaic cur- 
rent could be passed through water, and that in passing- 
through it decomposed a portion of the liquid into its 



224 ELECTRICITY AXD MAGNETISM part i 

constituent gases. These gases appeared in bubbles on 
the ends of the wires which led the current into and out 
of the liquid ; bubbles of oxygen gas appearing at the 
point where the current entered the liquid, and hydrogen 
bubbles where it left the liquid. It was soon found that 
a great many other liquids, particularly dilute acids and 
solutions of metallic salts, could be similarly decomposed 
by passing a current through them. 

236. Electrolysis. — To this process of decomposing 
a liquid by means of an electric current Faraday gave 
the name of electrolysis (/.e. electric analysis) ; and those 
substances which are capable of beuig thus decomposed 
or '• electrolyzed " he termed electrolytes. 

The ends of the wires leading from and to the battery 
are called electrodes ; and to distinguish them, that by 
which the current enters is called the anode, that by 
which it leaves the kathode. The vessel in which a 
liquid is placed for electrolysis is termed an electrolytic 
cell. 

237. Electrolysis of Water. — Returning to the de- 
composition of water, we may remark that perfectly 
pure water appears not to conduct, but its resistance is 
greatly reduced by the addition of a few. drops of sul- 
phuric or of hydrochloric acid. The apparatus shown in 
Fig. 138 is suitable for this purpose. Here a battery of 
two cells (those shown are circular Bunsen's cells) is seen 
with its poles connected to two strips of metallic platinum 
as electrodes, which project up into a vessel containing 
the acidulated water. Two tubes closed at one end, 
which have been previously filled with water and in- 
verted, receive the gases evolved at the electrodes. 
Platinum is preferred to other metals such as copper or 
iron for electrodes, since it is less oxidizable and resists 
every acid. It is found that there is almost exactly twice 
as much hydrogen gas (by volume) evolved at the kathode 
as there is of oxygen at the anode. This fact corresponds 
with the known chemical composition of water, which is 



CHAP. Ill ELECTROLYSIS OF WATER 



225 



produced by combining together these two gases in the 
proportion of two vohimes of the former to one of the 
latter, Tlie proportions of gases evolved, how^ever, are 
not exactly two to one, for at first a very small quantity 
of the hydrogen is absorbed or " occluded " by the plati- 
num surface, while a more considerable proportion of the 
oxygen — about 1 per cent — is given off in the denser 




Fig. 138. 

allotropic form of ozone, which occupies less space and 
is also slightly soluble in the water. When a sufficient 
amount of the gases has been evolved and collected 
they may be tested; the hydrogen by showing that it 
will burn, the oxygen by its causing a glowing spark 
on the end of a splinter of wood to burst into flame. 
If the two gases are collected together in a common 
receiver, the mixed gas will be found to possess the well- 
known explosive property of mixed hydrogen and oxygen 
gases. The chemical decomposition is expressed in the 
following equation : 



H,0 


z= 


H. 


+ 





Water 


jaelds 
Q 


2 vols, of Hydrogen 


and 


1 vol. of Oxygen 



226 ELECTEICITY AND MAGNETISM part i 

238. Electrolysis of Sulphate of Copper. — We will 
take as another case the electrolysis of a solution of the 
well-known "blue vitriol" or sulphate of copper. If a 
few crystals of this substance are dissolved in v/ater a 
blue liquid is obtained, which is easily electrolyzed be- 
tween two electrodes of platinum foil, by the current from 
a single cell of any ordinary battery. The chemical for- 
mula for sulphate of copper is CUSO4. The result of the 
electrolysis is to split it up into two parts. Metallic 
copper is carried forward by the current and deposited 
in a film upon the kathode, leaving behind at the anode 
" sulphion," an easily decomposed compound of sulphur 
and oxygen, which is immediately acted upon by the 
water forming sulphuric acid and oxygen. This oxygen 
is liberated in bubbles at the anode. The chemical 
changes are thus expressed : 



CuSO^ 


= 


Cu 4- 


SO, 


Sulphate of Copper 


becomes 


Copper and 


Sulphion ; 


SO4 -f HgO 


= 


H2SO4 


+ 


Sulphion and water 


produce 


Sulphuric acid 


and Oxygen 



In this way, as the current continues to flow, copper 
is continually withdrawn from the liquid and deposited 
on the kathode, and the liquid gets more and more acid. 
If copper electrodes are used, instead of platinum, no 
oxygen is given off at the anode, but the copper anode 
itself dissolves away into the liquid at exactly the same 
rate as the copper of the liquid is deposited on the 
kathode. 

239. Anions and Kations. — The atoms which thus 
are severed from one another and carried invisibly by 
the current to the electrodes, and there deposited, are 
obviously of two classes ; some are left behind at the 
anode, others are carried forward to the kathode. Fara- 
day gave the name of ions to these wandering atoms; 
those left at the anode being anions, and those going 
to the kathode being kations. Anions are sometimes 



CHAP. Ill LA^YS OF ELECTROLYSIS 227 

regarded as " electronegative," because they move as if 
attracted toNvard the + pole of the battery, while the 
kations are regarded as "electropositive." Hydrogen 
and the metals are kations, moving apparently with the 
direction assumed as that of the current, and are de- 
posited where the current leaves the electrolytic cell. 
The anions are oxygen, chlorine, etc. When, for ex- 
ample, chloride of tin is electrolyzed, metallic tin is 
deposited on the kathode, and chlorine gas is evolved at 
the anode. 

240- Quantitative Laws of Electrolysis. 

(i.) The amount of chemical action is equal at all points 
of a circuit. If two or more electrolytic cells are placed 
at different points of a simple circuit the amount of 
chemical action will be the same in all, for the same 
quantity of electricity flows past every point of the cir- 
cuit in the same time. If all these cells contain acidu- 
lated water, the quantity, for example, of hydrogen set 
free in each will be the same ; or, if they contain a solu- 
tioQ of sulphate of copper, identical quantities of copper 
will be deposited in each. If some of the cells contain 
acidulated water, and others contain sulphate of copper, 
the weights of hydrogen and of copper will not be equal, 
but will be in chemically equivalent quantities. 

(ii.) The amount of an ion liberated at an electrode in 
a given time is proportional to the strength of the current. 
A current of two amperes yi[\]\. cause just twice the quan- 
tity of chemical decomposition to take place as a current 
of one ampere would do in the same time. 

(iii.) The amount of an ion liberated at an electrode in 
one second is equal to the strength of the current multiplied 
by the " electro-chemical equivalent " of the ion. It has been 
found by experiment that the passage of one coidomb of 
electricity through water liberates -000010384 gramme 
of hydrogen. Hence, a current the strength of which 
is C {amperes) will liberate C x -000010381 grammes 
of hydrogen per second. The quantity -000010384 is 



228 ELECTRICITY AXD MAGXETISM part i 

called the electrochemical equivalent of hydrogen. The 
" electrochemical equivalents " of other elements can be 
easily calculated if their chemical " equivalent " is known. 
Thus the chemical "equivalent"* of copper is 31-59; 
multiplying this by -000010384 we get as the electro- 
chemical equivalent of copper the value -0003281 
(gramme). 

Table of Electrochemical Equivalents, etc. 



Element. 



Atomic 

Weight. 


Val- 
ency. 


Chemical 
Equiva- 
lent. 


1 


1 


1 


39-03 


1 


39-03 


23- 


1 


23- 


196-2 


3 


65-4 


107-67 


1 


107-67 


63-18 


2 


31-59 


63-18 


1 


63-18 


199-8 


2 


99-9 


199-8 


1 


199-8 


117-8 


4 


29-45 


117-8 


2 


5S-9 


55-9 


2 


27-95 


55-9 


(3) 


18-64 


58-6 


2 


29-3 


64-9 


2 


32-45 


206-4 


2 


103-2 


15-96 


2 


7 -93 


35-37 


1 


35-37 


126-54 


1 


126-54 


79-76 


1 


79-76 


14-01 


3 


4-67 



Electrochemical 

Equivalent 

(grammes 

per coulomb). 



Electropositive - 

Hydrogen . 

Potassium . 

Sodium 

Gold . 

Silver . 

Copper (Cupric) 
" (Cuprous) 

Mercury (Mercuric) 
" (Mercurous) 

Tin (Stannic) 
" (Stannous) 

Iron (Ferrous) 
" (Ferric) 

Xickel . 

Zinc . 

Lead . 
Electronegative 

Oxygen 

Chlorine 

Iodine . 

Bromine 

Nitrogen 



0-000010384 

0-0004053 

0-00023SS 

0-0006791 

0-OOlllSl 

0-0003281 

0-0006562 

0-0010374 

0-00-20748 

0-0003058 

0-0006116 

0-0002902 

0-0001935 

0-0003043 

0-00033698 

0-0010716 

0-00008286 

0-0003673 

0-0013140 

0-000S2S2 

0-00004849 



* The chemical equivalent must not be confounded with the atomic 
weight. The atomic weight of copper is 63, that is to say, its atoms are 63 
times as heavy as atoms of hvdrogen. But in chemical combinations one 



CHAP. Ill VOLTAMETER 229 

241. Weight of Element deposited. — The following 
equation embodies the rule for finding the weight of any 
given ion disengaged fi'om an electrolytic solution during 
a known time by a current of known strength. Let C be 
the current (reckoned in amperes), t the time (in seconds), 
z the electrochemical equivalent, and iv the weight (in 
gTammes) of the element liberated; then 

w = zCt, 

or, in words, the weight (in grammes) of an element depos- 
ited by electrolysis is found by multiplying its electrochemical 
equivalent by the strength of the current (in amperes), and 
by the time (in seconds), during which the current continues 
to flow. 

Example. — A current from five Daniell's cells was passed 
through two electrolytic cells, one containing a solution 
of silver, the other acidulated water, for ten minutes. 
A tangent galvanometer in the circuit showed the 
strength of the current to be "5 amperes. The weight 
of silver deposited will be 0-001118 X -5 x 10 X 60 
= 0'3354 gramme. The weight of hydrogen evolved 
in the second cell will be -000010384: X '5 X 10 X 60 
= O'OOollo gramme. 

242. Voltameters. — The second of the above laws, 
that the amount of an ion liberated in a given time is 
proportional to the current, is sometimes known as Fara- 
day's Law, from its discoverer. Faraday pointed out that 
it affords a chemical means of measuring currents. He 
gave the name of voltameter to an electrolytic cell arranged 
for the purpose of measuring the current by the amount 
of chemical action it effects. 

243. Water-Voltameter. — The apparatus shown in 
Fig. 138 might be appropriately termed a Water- Vol- 

atom of copper replaces, or is "worth," two atoms of hydrogen ; hence the 

weight of copper equivalent to 1 of hydrogen is %3- = 31^. In all cases the 

. , << . , ,, . ,, ,. . atomic weight „, , ^ , , 

chemical equivalent" is the quotient ^ -. Ihe above table 

* ^ valency 

gives full statistical information. 



230 ELECTRICITY AND MAGNETISM part i 

tameter, provided the tubes to collect the gases be grad- 
uated, so as to measure the quantities evolved. The 
weight of each measured cubic centimetre of hydrogen 
(at the standard temperatiu*e of 0° C, and pressure of 
760 millims.) is known to be -00008988 grammes. Hence, 
if the number of cubic centimetres liberated during a 
given time, by a current of unknown strength be ascer- 
tained, the mean strength of the cm'rent can be calculated 
by first reducing the volume to weight, and then divid- 
ing by the electrochemical equivalent, and by the time. 
Each coulomb of electricity liberates in its flow -1155 
cubic centimetres of hydrogen, and -0577 c.c. of oxygen. 
If these gases are collected together in a mixed-gas volta- 
meter there will be -1732 c.c. of the mixed gases evolved 
for every coulomb of electricity which passes. To decom- 
pose 9 grammes of water, liberating 1 gramme of H and 
8 grammes of O, requires 96,302 coulombs to be sent 
through the liquid with an electromotive-force of at least 
1-47 volts (see Art. 487). 

244. Copper and Silver Voltameters. — As mentioned 
above, if sulphate of copper is electrolyzed between two 
electrodes of copper, the anode is slowly dissolved, and 
the kathode receives an equal quantity of copper as a 
deposit on its surface. One coulomb of electricity will 
cause -0003281 gramme to be deposited ; and to deposit 
one gTamme weiglit requires a total quantity of 3048 
coulombs to flow through the electrodes. A current of 
one ampere deposits in one hour 1-177 grammes of copper, 
or 4-0248 grammes of silver. 

By weighing one of the electrodes before and after 
the passage of a current, the gain (or loss) will be pro- 
portional to the quantity of electricity that has passed. 
In 1879 Edison, the inventor, applied this method for 
measuring the quantity of electricity supplied to houses 
for electric lights in them ; a small copper voltameter 
being placed in a branch of the circuit which supplied 
the house, to serve as a meter. Various other kinds of 



CHAP. Ill COMPARISON OF INSTRUMENTS 



231 




Fig. 139. 



supply meters have been proposed, having clockwork 
counters, rolling integrating disks, and other mechanical 
devices to add up the total quantity of electricity con- 
veyed by the current (see Art. 442). 

245. Comparison of Voltameters with Galvanometers. 
— It will be seen that both Galvanometers and Voltameters 
are intended to measure the strength of currents, one 
by magnetic, the other by chemical means. Faraday 
demonstrated that the magnetic and the chemical actions 
of a current are propor- 
tional to one another. In 
Fig. 139 is show^n a circuit 
that is branched so that 
the current divides, part 
going through a branch 
of small resistance r and 
part through a branch of 
larger resistance R. The 
current wdll divide, the 
greater part going by the 
path of lesser resistance. 
Three amperemeters are 
used. It wdll be found 
that the number of amperes 
in the main circuit is equal to the sum of the amperes 
in the two branches. In Fig. 140 the three ampere- 
meters have been replaced by three copper voltameters. 
The weight of copper deposited in the voltameter A in 
the main circuit will be found to be equal to the sum of 
the weights deposited in B and C in the two branches. 
A galvanometer shows, however, the strength of the cur- 
rent at any moment, and its variations in strength from 
one moment to another, by the position of the needle. 
In a voltameter, a varying current may liberate the 
atoms of copper or the bubbles of gas rapidly at one 
moment, and slowly the next, but all the varying quan- 
tities will be simply added together in the total yield. 




232 ELECTRICITY AND MAGNETISM part i 

In fact, the voltameter gives us the "time integral" of 
the current. It tells us icTiat quantity of electricity has 
flowed through it during the experiment, rather than 
how strong the current luas at any one moment. 

246. Chemical Test for Weak Currents. — A very 
feeble current suffices to produce a perceptible amount 
of change in certain chemical substances. If a few crys- 
tals of the white salt iodide of potassium are dissolved in 
water, and then a little starch paste is added, a very sen- 
sitive electrolyte is obtained, which turns to a dark blue 
colour at the anode when a very weak current passes 
tlii'ough it. The decomposition of the salt liberates 
iodine at the anode, which, acting on the starch, forms a 
coloured compound. White blotting-paper, dipped into 
the prepared liquid, and then laid on the kathode and 
touched by the anode, affords a convenient way of exam- 
ining the discoloration due to a current. A solution of 
ferrocyanide of potassium affords when using an anode 
of iron the well-known tint of Prussian blue. Bain 
proposed to utilize this in a Chemical Writing Tele- 
graph, the short and long currents transmitted along 
the line being thus recorded in blue marks on a strip of 
prepared paper, drawn along by clockrvork under an 
iron stylus joined to the positive wire. Faraday showed 
that chemical discoloration of paper moistened with 
starch and iodide of potassium was produced by the 
X:)assage of electricity from sources of all different kinds 
— frictional, voltaic, thermo-electric, and magneto-elec- 
tric, — even by that evolved by the Torpedo and the 
Gymnotus. In fact, he relied on this clnemical test as 
one proof of the identity of the different kinds. 

247. Internal and External Actions. — In an earlier 
lesson it was shown that the quantit}' of chemical action 
inside the cells of the battery was proportional to the 
current. Hence, Law (i.) of Art. 240 applies both to 
the portion of the circuit within the battery and to that 
without it. 



REVERSIBILITY OF CELLS 233 



Suppose 3 Daniell's cells are being employed to decompose 
water in a voltameter. Then while 1 gramme weight (11,126 
cub. centims.) of hydrogen and 8 grammes (5563 c.c.) of oxygen 
are set free in the voltameter, 31-5 grammes of copper will be 
deposited in each cell of the battery, and (neglecting loss by local 
action), 32'5 grammes of zinc will be dissolved in each cell. 

248. Reversibility. — It will therefore be evident 
that the electrolytic cell is the converse of the voltaic cell. 
The chemical work done in the voltaic cell furnishes the 
energy of the current which that cell sets up in the 
circuit. In the electrolytic cell chemical work is per- 
formed, the necessary energy being furnished by the cur- 
rent of electricity w^hich is 
sent into the cell from an 
independent battery or 
other source. It is im- 
portant to note the bearing 
of this with respect to the 
energy of the ckcuit. Sup- 
pose a current of strength 

C to flow through a cell of ^n.. l \ k i^MF opposes current. 




EMF helps current. 
Energy enters circuit. 




which the electromotive- „ ^^^^]Energy leaves circuit. 

force is E, and which acts 
in the same direction as Fig. 141. 

the current. The energy 

given to the circuit per second by this cell will be (Art. 
435) the product of C and E; the chemical energy of 
the voltaic cell entering the circuit at the place where 
the chemical action is going on. In Fig. 141 the current 
is indicated by the arrows with thick shafts, the electro- 
motive-force by the feathered arrow. For example, if 
10 amperes flow through a Daniell cell acting with 1-1 
volts of electromotive-force, the power given out by the 
cell is 11 ivatts (Art. 435). But if the cell be so con- 
nected into the circuit, as in Case II. of Fig. 141, that 
the E.M.F. of the cell opposes the current that is being- 
driven along the circuit, then the energy per second 



234 ELECTRICITY AND MAGNETIS:M part i 

will be the product of C and — E, or — CE, the negative 
sign indicating that the circuit is losing energy, part of 
its energy being absorbed in the cell in doing chemical 
work. If current is sent backwards through a Daniell 
cell the chemical processes are reversed, copper is dissolved 
and zinc is deposited. But all cells are not reversible in 
their chemical action. 

A theory of electrolysis, and some examples of its 
application, are given in Art. 488 on Electro-chemistry. 



Lessox XX. — Physical and Physiological Effects of the 
Current 

249. Molecular Actions. — Metal conductors, when 
subjected to the prolonged action of currents, undergo 
slow molecular changes. Wires of copper and brass 
gradually become brittle under its influence. During 
the passage of the current through metallic wires their 
cohesion is temporarily lessened, and there also appears 
to be a decrease in their coeflicient of elasticity. It was 
thought by Edlund that a definite elongation could be 
observed in strained wires when a cm-rent was passed 
through them; but it has not yet been satisfactorily 
shown that this elongation is independent of the elonga- 
tion due to the heating of the wire owing to the resistance 
it opposes to the current. 

250. Electric Osmose. — Porret observed that if a 
strong current is led into certain liquids, as if to electro- 
lyze them, a porous partition being placed between the 
electrodes, the current mechanically carries part of the 
liquid through the porous diaphragm, so that the liquid 
is forced up to a higher level on one side than on the 
other. This phenomenon, known as electric osmose, is 
most manifest when badly-conducting liquids, such as 
alcohol and bisulphide of carbon, are used. The transfer 
through the diaphragm takes place in the direction of 



CHAP. Ill YAKIOUS EFFECTS OF CUKRENTS 235 

the current; that is to say, the liquid is higher about 
the kathode than round the anode. 

251. Electric Distillation. — Closely connected with 
the preceding phenomenon is that of the electric distilla- 
tion of liquids. It was noticed by Beccaria that an elec- 
trified liquid evaporated more rapidly than one not elec- 
trified. Gernez has recently shown that in a bent closed 
tube, containing two portions of liquid, one of which is 
made highly + and the other highly — , the liquid passes 
over from + to — . This apparent distillation is not due 
to difference of temperature, nor does it depend on the 
extent of surface exposed, but is effected by a slow creep- 
ing of the liquid along the interior surface of the glass 
tubes. Bad conductors, such as turpentine, do not thus 
pass over. 

252. Diaphragm Currents. — Professor Quincke dis- 
covered that a current is set up in a liquid when it is 
forced by pressure through a porous diaphragm. This 
phenomenon may be regarded as the converse of electric 
osmose. The E.M.F. of the current varies with the press- 
ure and with the nature of the diaphragm. When water 
w^as forced at a pressure of one atmosphere through sul- 
phur, the difference of potential was over 9 volts. With 
diaphragms of porcelain and bladder the differences were 
only '35 and -01 volts respectively. 

253. Electro-Capillary Phenomena. — If a horizontal 
glass tube, turned up at the ends, be filled with dilute 
acid, and a single drop of mercmy be placed at about the 
middle of the tube, the passage of a current through the 
tube will cause the drop to move along towards the nega- 
tive pole. It is believed that the liberation of very small 
quantities of gas by electrolysis at the surface where the 
mercury and acid meet alters the surface-tension very 
considerably, and thus a movement results from the cap- 
illary forces. Lippmann, Dewar, and others have con- 
structed upon this principle capillary electrometers, in 
which the pressure of a column of liquid is made to bal- 



236 ELECTRICITY AND MAGNETISM part i 

ance the electro-capillary force exerted at the surface of 
contact of mercuiy and dilute acid, the electro-capillary 
force being nearly proportional to the electromotive-force 
when this does not exceed one volt. Fig. 142 shows the 
capillary electrometer of Dewar. A glass tube rests hori- 
zontally between two glass dishes in which holes have 




Fig. 142. 

been bored to receive the ends of the tube. It is filled 
with mercury, and a single drop of dilute acid is placed 
in the tube. Platinum wires to serve as electrodes dip 
into the mercury in the dishes. An E.M.F. of only gig- 
volt suffices to produce a measurable displacement of the 
drop. The direction of the displacement varies with 
that of the current. 

254. Physiological Actions. — Currents of electricity 
passed through the limbs affect the nerves with certain 
painful sensations, and cause the muscles to undergo 
involuntary contractions. The sudden rush of even a 
small charge of electricity from a Leyden jar charged to 
a high potential, or from an induction coil (see Fig. 135), 
gives a sharp and painful sliock to the system. The cur- 
rent from a few strong Grove's cells, conveyed through 
the body by grasping the terminals with moistened 
hands, gives a very different kind of sensation, not at 
all agreeable, of a prickling in the joints of the arms 
and shoulders, but not producing any spasmodic con- 
tractions, except it be in nervous or weakly persons, 
at the sudden making or breaking of the circuit. The 
difference between the two cases lies in the fact that 
the tissues of the body offer a very considerable resist- 



CHAP. Ill PHYSIOLOGICAL EFFECTS 237 

ance, and that the difference of potential in the former 
case may be many thousands of volts ; hence, though 
the actual quantity stored up in the Leyden jar is very 
small, its very high E.M.F. enables it at once to over- 
come the resistance. The battery, although it might, 
when M'orking through a good conductor, afford in one 
second a thousand times as much electricity, cannot, 
when working through the high resistance of the body, 
transmit more than a small fraction, owing to its limited 
E.M.F. 

After the discovery of the sliock of the Leyden jar by 
Cunaeus in 1TJ:5 many experiments were tried. Louis 
XV. of France caused an electric shock from a battery of 
Leyden jars to be administered to 700 Carthusian monks 
joined hand in hand, with prodigious effect. Franklin 
killed a turkey by a shock from a Leyden jar. 

In 1752 Sulzer remarked that " if you join two pieces 
of lead and silver, and then lay them upon the tongue, 
you will notice a certain taste resembling that of green 
vitriol, while each piece apart produces no such sensa- 
tion." This galvanic taste, not then suspected to have 
any connexion with electricity, may be experienced by 
placing a silver coin on the tongue and a steel pen under 
it, the edges of them being then brought into metallic 
contact. The same taste is noticed if the two wires from 
the poles of a single voltaic cell are placed in contact 
with the tongue. 

Ritter discovered that a feeble current transmitted 
through the eyeball produces the sensation as of a bright 
flash of light by its sudden stimulation of the optic nerve. 
A stronger current transmitted by means of moistened 
conductors attached to the battery terminals gave a sen- 
sation of blue and green colours in flowing between the 
forehead and the hand. Von Helmholtz, repeating this 
experiment, observed only a wild rush of colour. Dr. 
Hunter saw" flashes of light when a piece of metal placed 
under the tongue was touched against another which 



238 ELECTRICITY AND MAGNETISM pakt i 

touched the moist tissues of the eye. Yolta and Ritter 
heard musical sounds when a current was passed through 
the ears ; and Humboldt found a sensation to be produced 
in the organs of smell when a current was passed from the 
nostril to the soft palate. Each of the specialized senses 
can be stimulated into activity by the cm-rent. Man pos- 
sesses no specialized sense for the perception of electrical 
forces, as he does for light and for sound ; but there is no 
reason for denying the possibility that some of the lower 
creatures may be endowed with a special electrical sense. 

The following expeiiment shows the effect of feeble 
currents on cold-blooded creatures. If a copper (or silver) 
coin be laid on a piece of sheet zinc, and a common garden 
snail be set to crawl over the zinc, directly it comes into 
contact with the copper it will suddenly pull in its horns, 
and shrink in its body. If it is set to crawl over two 
copper wires, which are then placed in contact with a 
feeble voltaic cell, it immediately announces the estab- 
lishment of a current by a similar contraction.* 

255. Muscular Contractions. — In 1678 Swammer- 
dam showed to the Grand Duke of Tuscany that when 
a portion of muscle of a frog's leg hanging by a thread 
of nerve bound with silver wu'e was held over a copper 
support, so that both nerve and wire touched the copper, 
the muscle immediately contracted. More than a century 
later Galvani's attention was drawn to the subject by 
his observation of spasmodic contractions in the legs of 
freshly-killed frogs under the influence of the "return- 
shock " experienced every time a neighbom'ing electric 
machine was discharged. Unaware of Swammerdam's 
experiment, he discovered in 1786 the fact (alluded to in 
Art. 163 as leading ultimately to the discovery of the 
Voltaic Pile) that when nerve and muscle touch two 
dissimilar metals in contact with one another a contrac- 
tion of the muscle takes place. The limbs of the frog, 

* It will scarcely be'credited that a certain Jules Alix once seriously pro- 
posed a system of telegraph}- based on this physiological phenomenon. 



CHAP. Ill MUSCULAR CONTRACTIONS 239 

prepared as dii'ected by Galvani, are shown in Fig. 143. 
After the animal has been killed the hind limbs are de- 
tached and skinned ; the crural nerves and their attach- 
ments to the lumbar vertebrae remaining. For some 
hom's after death the limbs retain their contractile povv^er. 
The frog's limbs thus prepared form an excessively deli- 
cate galvanoscope : with them, for example, the excessively 




Fig. 143. 

delicate induction-currents of the telephone (Lesson LIII.) 
can be shown, though the most sensitive galvanometers 
barely detect them. Galvani and Aldini proved that 
other creatures undergo like effects. With a pile of 100 
pairs Aldini experimented on newly-killed sheep, oxen, 
and rabbits, and found them to suffer spasmodic muscular 
contractions. Humboldt proved the same on fishes ; and 
Zanotti, by sending a current through a newly-killed 
grasshopper, caused it to emit its familiar chirp. Aldini, 



240 ELECTRICITY AND MAGNETISM part i 

and later Dr. Ure of Glasgow, experimented on the bodies 

of executed criminals, with a success terrible to behold. 
The facial muscles underwent horrible contortions, and 
the chest heaved with the contraction of the diaphragm. 
The small muscles attached to the roots of the hairs of 
the head ajDpear to be markedly sensitive to electrical 
conditions from the readiness with which electrification 
causes the hair to stand on end. 

The resistance of the human body to the flow of electric 
current through it depends mainly on the drjmess of the 
skin. It may vary from 10,000, down to 300 ohms when 
the skin is moist. From experiments made in America 
in connexion with the execution of criminals, it was 
found that the average resistance of the human body is 
2500 olims, and that 3000 (alternating) volts applied 
between the head and spine caused instantaneous death. 

A current of as much as 20 milliamperes produces 
terrible muscular contractions, whilst a current of 2 
amperes traversing a vital part is almost certainly fatal. 
The effect of the current is twofold; in the first place it 
acts upon the nerves, causing spasms, secondly it destroys 
the tissue either by burning or by electrolysis, the blood 
becoming coagulated. To restore a person who has been 
rendered msensible by an electric shock, all the same 
restoratives should be used as for a person drowned. 

256. Conditions of Muscular Contraction. — To pro- 
duce muscular contraction the current must traverse a 
portion of the nerve longitudinally. In a freshly-prepared 
frog the current causes a contraction only momentarily 
when the circuit is made or broken. A rapidly interrupted 
current will induce a second contraction before the first 
has had time to pass off, and the muscle may exhibit thus 
a continuous contraction resembling tetanus. The pre- 
pared frog after a short time becomes less sensitive, and 
a " direct " current (that is to say, one passing along the 
nerve in the direction from the brain to the muscle) only 
produces an effect when cu'cuit is made, while an "in- 



CHAP. Ill ANIMAL ELECTEICITY 241 

verse " current only produces an effect when the circuit 
is broken. Matteucci, who observed this, also discovered 
by experiments on living animals that there is a distinction 
between the conductivity of sensory and motor nerves, — 
a " du-ect " cui-rent affecting the motor nerves on making 
the circuit, and the sensory nerves on breaking it ; while 
an " inverse " current produced inverse results. Little is, 
however, yet known of the conditions of conductivity of 
the matter of the nerves ; they conduct better than mus- 
cular tissue, cartilage, or bone ; but of all substances in 
the body the blood conducts best. Powerful currents 
doubtless electrolyze the blood to some extent, coagulat- 
ing it and the albumin it contains. The power of con- 
tracting under the influence of the current appears to be 
a distinguishing property of protoplasm wherever it occurs. 
The amoeba, the most structureless of organisms, suffers 
contractions. Ritter discovered that the sensitive plant 
shuts up when electrified, and Burdon Sanderson has 
shown that this property extends to other vegetables, 
being exhibited by the carnivorous plant, the Dionaea or 
Venus' Fly Trap. 

257. Animal Electricity. — Although, in his later 
writings at least, Galvani admitted that the electricity 
thus operating arose from the metals employed, he insisted 
on the existence of an animal electricity resident in the 
muscular and nervous structures. He showed that con- 
tractions could be produced without using any metals at 
all by merely touching a nerve at two different points 
along its length with a morsel of muscle cut from a living 
frog ; and that a conductor of one metal when joining a 
nerve to a muscle also sufficed to cause contraction in the 
latter. Galvani and Aldini regarded these facts as a 
disproof of Volta's contact-theory. Volta regarded them 
as proving that the contact between nerve and muscle 
itself produced (as in the case of two dissimilar metals) 
opposite electrical conditions. Nobili, later, showed that 
when the nerve and the muscle of the frog were respec- 



242 ELECTRICITY AND MAGNETISM part i 

tively connected by a water-contact with the terminals of 
a delicate galvanometer, a current is produced which lasts 
several hours : he even arranged a number of frogs' legs 
in series, like the cells of a battery, and thus increased the 
current. Matteucci showed that through the muscle alone 
there may be an electromotive-force. Du Bois Reymond 
has shown that if the end of a muscle be cut across, the 
ends of the muscular fibres of the transverse section are 
negative, and the sides of the muscular fibres are positive, 
and that this difference of potential will produce a current 
even while the muscle is at rest. To demonstrate this he 
employed a fine astatic galvanometer with 20,000 turns 
of wire in its coils ; and to obviate errors arising from the 
contact of the ends of the wires with the tissues unpolariz- 
dble electrodes were used, made by plunging terminal zinc 
points into a saturated solution of sulphate of zinc, con- 
tained in a fine glass tube, the end of which was stopped 
with a porous plug of moistened china clay. Xormal 
muscle at rest shows no current whatever between its 
parts. Injured muscle at rest shows a current from the 
injured toward the uninjured part (returning toward the 
injured part through the galvanometer). Xormal muscle 
when active shows a current from the active part toward 
the resting part. Du Bois Reymond obtained currents 
from his own muscles by dipping the tips of his fore- 
fingers into two cups of salt water communicating with 
the galvanometer terminals. A sudden contraction of 
the muscles of either arm produced a current from the 
contracted toward the uncontracted muscles. Dewar 
has shown that when light falls upon the retina of the 
eye an electric cm'rent is set up in the optic nerve. 
In the skin, and especially in the skm of the com- 
mon eel, there is an electromotive-force from without 
inwards. 

258. Surgical Applications. — Electric currents have 
been successfully employed as an adjunct in restoring 
persons rescued from drowning; the contraction of the 



CHAP. Ill SURGICAL APPLICATIONS 243 

diaphragm and chest muscles serving to start respiration. 
Since the discovery of the Leyden jar many attempts 
have been made to establish an electrical medical treat- 
ment. Discontinuous currents, particularly those fur- 
nished by small induction-coils and magneto-electric 
machines, are employed by practitioners to stimulate the 
nerves in paralysis and other affections. Electric cur- 
rents should not be used at all except with great care, 
and under the direction of regularly-trained surgeons. 
It is not out of place to enter an earnest caution on this 
head against the numerous quack doctors who deceive 
the unwary wdth magnetic and galvanic " appliances." 
In many cases these much-advertised shams have done 
incalculable harm : in the very few cases where some 
fancied good has accrued the curative agent is probably 
not magnetism, but flannel ! 

The usual pathological dose of current is from 2 to 10 
milliamperes. Apparatus pretending to cure, and incapa- 
ble of furnishing such currents, is worthless. Continuous 
currents appear to produce a sedative effect around the 
anode, w^hich is of service in neuralgia and painful affec- 
tions, and an increase in irritability around the kathode, 
useful in cases of paralysis. The continuous current is 
also employed electrolytically to disperse tumours. Al- 
ternate currents, and rapidly interrupted uni-directional 
currents stimulate the nerves. 



JPart Secontr 

CHAPTER IV 

ELECTROSTATICS 



Lessox XXI. — Theory of Potential 

259. By the lessons in Chapter I. the student wiU 
have obtained some elementary notions upon the exist- 
ence and measui-ement of definite quantities of electricity. 
In the present lesson, which is both one of the hardest 
and one of the most important to the beginner, and 
which he must therefore study the more carefully, the 
laws which concern the magnitude of electrical quantities 
and their measurement are more fully explained. In no 
branch of knowledge is it more true than in electricity, 
that "science is measurement." That part of the science 
of electricity which deals with the measurement of charges 
of electricity is called Electrostatics. We shall begin by 
discussing first the simple laws of electric force, which 
were brought to light in Chapter I. by simple experi- 
mental means. 

260. First Law of Electrostatics. — Electric charges 
of similar sign repel one another, but electric charges of op- 
posite signs attract one another. The fundamental facts 
expressed in this Law were fully explained in Lesson I. 

244 



CHAP. IV LAW OF INVERSE SQUARES 245 

Though familiar to the student, and apparently simple, 
these facts require for theu' complete explanation the aid 
of advanced mathematical analysis. They will here be 
treated as simple facts of observation. 

261. Second Law of Electrostatics. — The force 
exerted between tico charges of electricity (supposing them 
to be collected at points or on two small spheres) is directly 
proportional to their product, and inversely proportional to 
the square of the distance between them. This law, discovered 
by Coulomb, and called Coulomb's Law, was briefly alluded 
to (on p. 21) in the account of experiments made with 
the torsion-balance; and examples were there given in 
illustration of both parts of the law. We saw, too, that 
a similar law held good for the forces exerted between 
two magnetic point-poles. Coulomb applied also the 
method of oscillations to verify the indications of the 
torsion-balance and found the results entirely confirmed. 
We may express the two clauses of Coulomb's Law in the 
following symbolic manner. Let / stand for the force, q 
for the quantity of electricity in one of the two charges, 
and q' for that of the other charge, and let r stand for 
the distance between them. Then, 

(1) /is proportional to q x q', 
and (2) /is proportional to — . 

These two expressions m.ay be combined into one ; 
and it is most convenient so to choose our units or 
standards of measurement that we may write our sym- 
bols as an equation : — 

/= 12M'. 

262. Unit of Electric Quantity. — If we are, how- 
ever, to write this as an equality, it is clear that we 
must choose our unit of electricity in accordance with 
the units already fixed for measuring force and distance. 



246 ELECTRICITY AND MAGNETISM part ii 

Electricians of all nations have agreed in adopting a 
system which is based upon three fundamental units : 
viz. the Centimetre for a unit of length ; the Gramme 
for a unit of mass ; the Second for a unit of time. Ail 
other units can be derived from these, as is explained 
in the note at the end of this lesson. l!»[ow, amongst 
the derived units of this system is the unit of force, 
named the Dyne, which is that force which, acting for 
one second on a mass of one gramme, imparts to it 
a velocity of one centimetre per second. Taking the 
dyne then as the unit of force, and the centimetre as the 
unit of length (or distance), we must find a unit of electric 
quantity to agree with these in our equation. It is quite 
clear that if q, q', and r were each made equal to 1 (that 
is, if we took two charges of value 1 each, and placed 

them one centimetre apart), the value of - — ^ would be 

1x1 

^ r- which is equal to 1. Hence we adopt, as our 

Definition of a Unit of Electricity,* the following, which 
we briefly gave at the end of Lesson XL One Unit of 
Electricity is that quantity which, tvhen placed at a distance 
of one centimetre (in air^ from a similar and equal quantity, 
repels it ivith a force of one dyne. 

An example will aid the student to understand the 
application of Coulomb's Law. 

Example. — Two small spheres, charged respectively with 
6 units and 8 units of + electricity, are placed 4 centi- 
metres apart ; find what force they exert on one 

another. By the formula, / = ^-^^, we find / = 

6X8 48 „ , 
-^ = ^ = 3 dynes. 

The force in the above example would clearly be a 
force of repulsion. Had one of these charges been 

* That is one unit, in the electrostatic system. It is only 5(JottjW?5?to of 
the quantity called 1 coulomb. 



CHAP. IV NOTIONS OF POTENTIAL 247 

negative, the product q x q' would have had a — value, 
and the answer would have come out as minus 3 dynes. 
The presence of the negative sign, therefore, prefixed to 
a force, will indicate that it is a force of attraction, whilst 
the + sign would signify a force of repulsion. 

The intensity of an electric field (Art. 266) being- 
measured by the force it exerts on a unit charge, it at once 
follows that at a distance of r (in air) from a charge q the 
intensity of the electric field due to that charge will be 
q/r'^. If the intervening medium be not air, but have a 
specific dielectric capacity k, the field will be only q/kr^. 

263. Potential. — We must next define the term 
potential, as applied to electric forces ; but to make the 
meaning plain a little preliminary explanation is necessary. 
Suppose we had a + charge on a small insulated sphere 
A (see Fig. IM), placed by itself far from all other 
electric charges and conductors. If we were to bring 
another positively-charged body B near it, A would repel 
B. But the repelling force would depend on the quantity 
of the new charge, and on the distance at which it was 

A P Q B'' B' 

Q.„„„ e -e e ©—- 

Fig. 144. 

placed. Suppose the new charge thus brought near to be 
one + unit ; when B was a long way off it would be 
repelled with a very slight force, and very little work 
need be expended in bringing it up nearer against the 
repelling forces exerted by A ; but as B was brought 
nearer and nearer to A, the repelling force would grow 
greater and greater, and more and more work would have 
to be done against these opposing forces in bringing up 
B. Suppose that we had begun at an infinite distance 
away, and that we pushed up our little test charge B from 
B' to B" and then to Q, and so finally moved it up to the 
point P, against the opposing forces exerted by A, we 



248 ELECTRICITY AND MAGNETISM part ii 

should have had to spend a certain amount of work; that 
work represents the potential * at the point P due to A. 
For the following is the definition of electric potential : — 
The potential at any point is the icork that must he spent 
upon a unit of positive electricity in bringing it up to that 
point from an infinite distance. Had the charge on A been 
a — charge, the force would have been one of attraction, 
in which case we should have theoretically to measure 
the potential at P, either by the opposite process of placing 
there a + unit, and then removing it to an infinite dis- 
tance against the attractive forces, or else by measuring 
the amount of work which would be done by a, + unit in 
being attracted up to P from an infinite distance. 

It can be shown that where there are more electrified 
bodies than one to be considered, the potential due to 
them at any point is the sum of the potentials (at that 
point) of each one taken separately. 

It can also be shown that the potential at a point P, 
near an electrified particle A, is equal to the quantity of 
electricity at A divided by the distance between A and P. 
Or, if the quantity be called q, and the distance r, the 
potential is q -^ r.f 

Proof. — First determine the difference of potential between 
point P and point Q due to a charge of electricity g on a small 
sphere at A. 

Call distance AP = r, and AQ =r'. Then PQ = r' — r. The 
difference of potential between Q and P is the looi^k done in 
moving a + unit from Q to P against the force ; and since 

* In its widest meaning the term " potential" must be understood as 
"power to do work." For if we have to do a certain quantity of work 
against the repelling force of a charge in bringing up a unit of electricity 
from an infinite distance, just so much Avork has the charge power to do, 
for it A\ill spend an exactly equal amount of work in pushing the unit of 
electricity back to an infinite distance. If Ave lift a pound five feet high 
against the force of gravity, the weight of the pound can in turn do five 
foot-pounds of work in falling back to the ground. 

t The complete proof Avould require an elementary application of the 
integral calculus, but an easy geometrical demonstration, sufficient for 
present purposes, is given below. 



CHAP. IV THEORY OF POTENTIAL 249 



work = (average) force X distance through which it is 
overcome 
Vp-VQ=/(;''-r). 

Force at P exerted by g on a + unit = q fr'^, 
and the force at Q exerted by g on a + unit = q/r'^. 

Suppose now that the distance PQ be divided into any number 

(n) of equal parts rri, r-ir^, r^r^, ^n-i^'- 

The force at r = q/r^. 

" " Vi = q/r-^ .... etc. 

Now since r^ may be made as close to r as we choose, if we 
only take n a large enough number, we shall commit no serious 



error in supposing that r X rj is a fair mean between ^2 and r-^ ; 
hence we may assume the average force over the short length 

from r to Vi to be — - 

Hence the work done in passing from Vi to r will be 



-(K) 



On a similar assumption, the work done in passing from r-i to 
Vi, will be 

= g ( — — — 1 , and that done from Vo to ro will be 

= gf — — — ) , etc., giving us n equations, of which the 
last will be the work done in passing from r' to r^-i 

Adding up all these portions of the work, the intermediate 



250 ELECTRICITY AND MAGNETISM part ii 



values of r cancel out, and we get for the work done in passing 
from Q to P 

Next suppose Q to be an infinite distance from A. Here 
r' = infinity, and — = 0. In that case the equation becomes 



r 

If there are a number of electrified particles at different 
distances from P, the separate values of the potential q/r 
due to each electrified particle separately can be found, 
and therefore tlie potential at P can he found hy dividing the 
quantity of each charge hy its distance from the point P, and 
then adding up together the separate amounts so obtained. 
The symbol Y is generally used to represent potential. 
The potential at P we will call Vp, then 

^P = ^ + p7 + ^+ etc. 

or yv=^l- 

This expression 21^/r represents the work done on or by 
a unit of + electricity when moved up to the given point 
P from an infinite distance, according as the potential at 
P is positive or negative. 

264. Zero Potential. — At a place infinitely distant 
from all electrified bodies there would be no electric forces 
and the potential would be zero. For purposes of conven- 
ience it is, however, usual to consider the potential of the 
earth as an arbitrary zero, just as it is convenient to con- 
sider " sea-level " as a zero from which to measure heights 
or depths (see Art. 269). 

265. Difference of Potentials. — Since potential repre- 
sents the work that must be done on a + unit in 
bringing it up from an infinite distance, the difference of 



CHAP, ir DIFFERENCE OF POTENTIALS 251 

potential between two points is the ivorh to he done on 
or by a + unit of electricity in carrying it from one point 
to the other. Thus if Yp represents the potential at P, 
and Vq the potential at another point Q, the difference of 
potentials Yp — Yq denotes the work done in moving up 
the + unit from Q to P. It is to be noted that since this 
value depends only on the values of the potential at P 
and at Q, and not on the values at intermediate points, 
the work done will be the same, whatever the path along 
which the particle moves from Q to P. In the same way- 
it is true that the expenditure of energy in lifting a 
pound (against the earth's attraction) from one jDoint to 
another on a higher level, will be the same whatever the 
path along which the pound is lifted. 

266. Electric Force. — The definition of "work" is 
the product of the force overcome into the distance 
through ivhich the force is overcome ; or work = force 

X distance through which it is overcome. 

Hence, if the difference of potential between two points 
is the work done in moving up our + unit from one 
point to the other, it foUows that the average electric 
force between those points will be found by dividing the 
work so done by the distance between the points; or 

^ ^ =f (the average electric force along the line 

PQ). The (average) electric force is therefore the rate 
of change of potential per unit of length. If P and Q 
are near together the force will be practically uniform 
between P and Q. The term electromotive intensity is 
sometimes used for the force in an electric field. 

We may represent this intensity of the electric field 
by supposing the number of electric lines per square 
centimetre to be drawn to represent the number of dynes 
of force on a + unit placed at the point. 

267. Equipotential Surfaces. ^ — A charge of elec- 
tricity collected on a small sphere acts on external bodies 
as if the charge were all collected into one point at its 



252 



ELECTRICITY AND MAGNETISM part ii 



centre.* We have seen that the force exerted by such a 
charge falls off at a distance from the ball, the force 
becoming less and less as the square of the distance 
increases. But the force is the same in amount at all 
points equally distant from the small charged sphere. 
And the potential is the same at all points that are 
equally distant from the charged sphere. If, in Fig. 145, 
the point A represents the sphere charged with q units of 



• ? ? 






Fiff. 146. 



electricity, then the potential at P, which we will call 
Vp, will be equal to q/r, where r is the distance from A 
to P. But if we take any other point at the same dis- 
tance from A its potential will also be q/r. ]^ow all the 
points that are the same distance from A as P is, will be 
found to lie upon the surface of a sphere whose centre is 
at A, and which is represented by the circle drawn through 
P, in Fig. 146. All round this chcle the potential will 
have equal values ; hence this circle represents an equi- 
potential surface. The work to be done in bringing u]3 
a + unit from an infinite distance will be the same, no 

* The student must be warned that this ceases to be true if other 
charges are brought very near to the sphere, for then the electricity will 
no longer be distributed uniformly over its surface. It is for this reason 
that we have said, in describing the measurement of electrical forces with 
the torsion balance, that "the balls must be very small in proportion to 
the distances between them." 



CHAP, iv^ EQUIPOTENTIAL SURFACES 253 

matter what point of this eqaipotential surface it is 
brought to, and to move it about from one point to 
another in the equipotential surface requires no further 
overcoming of the electrical forces, and involves therefore 
no further expenditure of work. At another distance, 
say at the point Q, the potential will have another value, 
and through this point Q another equipotential surface 
may be drawn. Suppose we chose Q so far from P that 
to push up a unit of + electricity against the repelling 
force of A required the expenditure of just one erg of 
work (for the definition of one erg see the Note on Units 
at the end of this lesson) ; there will be then unit 
difference of potential between the surface drawn through 
Q and that di'awn through P, and it will requu-e one 
erg of work to carry a + unit from any point on the one 
sm'face to any point on the other. In like manner we 
might construct a whole system of equipotential surfaces 
about the point A, choosing them at such distances that 
there should be unit difference of potential between each 
one and the next. The widths between them would get 
wider and wider, for, since the force falls off as you 
go fm'ther from A, you must, in doing one erg of work, 
bring up the + nnit through a longer distance against 
the weaker opposing force. 

The form of the equipotential surfaces about two small 
electrified bodies placed near to one another would not 
be spherical; and around a number of electrified bodies 
placed near to one another the equipotential surfaces 
would be highly complex in form. 

268. Lines of Force. — The electric force, whether 
of attraction or repulsion, always acts across the equi- 
potential surfaces in a direction normal to the surface. 
The lines which mark the direction of the resultant 
electric forces are sometimes called lines of electric force. 
In the case of the single electrified sphere the lines of 
force would be straight lines, radii of the system of equi- 
potential spheres. In general, however, lines of force are 



254 ELECTRICITY AND MAGNETISM part it 

curved; in this case the resultant force at any point 
would be in the direction of the tangent to the cui've at 
that point. Two lines of force cannot cut one another, 
for it is impossible ; the resultant force at a point cannot 
act in two du'ections at once. The positive direction 
along a line of force is that direction in which a small 
positively-charged body would be impelled by the electric 
force if free to move. A space bounded by a number of 
lines of force is sometimes spoken of as a tube of force. 
All the space, for example, round a small insulated 
electrified sphere may be regarded as mapped out into a 
number of conical tubes, each having their apex at the 
centre of the sphere. The total electric force exerted 
across any section of a tube of force is constant wherever 
the section be taken. 

269. Potential within a Closed Conductor. — The 
experiments related in Arts. 32 to 36 prove most con- 
vincingly that there is no electric force inside a closed 
conductor due to charges outside or on the surface of the con- 
ductor. !N"ow we have shown above that electric force is 
the rate of change of potential per unit of length. If 
there is no electric force there is no change of potential. 
The potential within a closed conductor (for example, a 
hollow sphere) due to charges outside or on the surface 
is therefore the same all over the interior ; the same as 
the potential of the surface. The surface of a closed con- 
ductor is necessarily an equipotential surface. If it were 
not at one potential there would be a flow of electricity 
from the higher potential to the lower, which would 
instantaneously establish equilibrium and reduce the 
whole to one potential. The student should clearly dis- 
tinguish between the sm'f ace-density at a point, and the 
potential at that point due to neighbouring charges of 
electricity. We know that when an electrified body is 
placed near an insulated conductor the nearer and farther 
portions of that conductor exhibit induced charges of 
opposite kinds. Yet all is at one potential. If the + 



CHAP. IT POTENTIAL INSIDE CONDUCTOES 255 

and — charges on the conductor had not separated by 
a moveinent of electricity from one side to the other, 
a difference of potential would exist between those sides 
because they are at different distances from the electri- 
fied body. But that is a state of affairs which could 
not continue in the conductor, for the difference of 
potential would cause electricity to flow until the com- 
bined potential due to the electrified body and the charges 
at the opposite sides was the same at every point in the 
conductor. 

The potential at any point in a conducting sphere 
(hollow or solid) due to an electrified particle A, situated 
at a point outside (Fig. 148), is equal to the quantity of 
electricity q at A divided by the distance between A and 
the centre of the sphere. For if B be the centre of the 
sphere, the potential at B due to q is q/r, where r = AB ; 
but all points in the sphere are at the same potential, 
therefore they are all at the potential q/r. 

The earth is a large conducting sphere. Its potential, 
due to a positive charge q near to its surface, is q/r, 
where r may be taken as the radius of the earth ; that 
is 636,000,000 centimetres. But it is impossible to pro- 
duce a + charge q without generating also an equal 
negative charge — 7 ; so the potential of the earth due 
to both charges is q/r — q/r = (see Art. 264). 

270. Law of Inverse Squares. — An important con- 
sequence follows from the absence of electric force inside 
a closed conductor due to a charge on its surface ; this 
fact enables us to demonstrate the necessary truth of the 
" law of inverse squares " which was first experimentally, 
though roughly, proved by Coulomb with the torsion 
balance. Suptpose a point P anywhere inside a hollow 
sphere charged with electricity (Fig. 147). The charge 
is uniform all over, and the quantity of electricity on 
any small portion of its surface will be proportional to 
the area of that portion. Consider a small portion of the 
surface AB. The charge on AB would repel a + unit 




256 ELECTEICITY AXD MAGXETISM paet ii 

placed at P with a certain force. Xow draw the lines 
AD and BC through P. and regard these as mapping ont 
a small conical surface of two sheets, having its apex at 
P: the small area CD will 
represent the end of the 
opposed cone, and the elec- 
tricity on CD will also act on 
the -f unit placed at P, and 
repel it. Xow these surfaces 
AB and CD. and the charges 
on them, will be directly pro- 
portional to the squares of 
their respective distances 
from P. If. then, the forces 
■^"^■■^''" which they exercise on P 

exactly neutralize one another (as experiment shows 
they do), it is clear that the electric force must fall off 
inversely as the squares of the distances; for the whole 
stirface of the sphere can be mapped ont similarly by 
imaginary cones drawn through P. The reasoning can 
be extended also to hollow conductors of any form. 

271. Capacity. — In Lesson IV. the student was 
given some elementary notions on the subject of the 
Capacity of conductors. We are now ready to give the 
precise definition. The Electrostatic Capacity of a con- 
ductor is measured by the quantity of electricity which must 
be imparted to it in order to raise its potential from zero to 
unity. A small conductor, such as an insulated sphere 
of the size of a pea. wiU not want so much as one unit 
of electricity to raise its potential from to 1; it is 
therefore of small capacity — while a large sphere will 
require a large quantity to raise its potential to the same 
degree, and would therefore be said to be of large capacity. 
If K stand for capacity, and Q for a quantity of electricity, 

K = ^ and KV = Q. 

This is equivalent to saying in words that the quantity 



CHAP. IV CAPACITIES OF SPHERES 257 

of electricity necessary to charge a given conductor to 
a given potential, is numerically equal to the product of 
the capacity into the potential through which it is raised. 
The capacity of an insulated body is affected by the pres- 
ence of neighbouring conductors. Whenever we speak 
of the capacity of a body, we mean of that body when 
isolated as well as insulated. 

272. Unit of Capacity. — A conductor that required 
only one unit of electricity to raise its potential from to 
1, would be said to possess unit capacity. A sphere one 
centimetre in radius possesses unit capacity ; for if it be 
charged with a quantity of one unit, this charge will 
act as if it were collected at its centre. 
At the surface, which is one centimetre / \ 

away from the centre, the potential, a / r \ 
which is measured as q/r, will be 1. @ ( • J 

Hence, as 1 unit of quantity raises it to ' \r " J 
unit 1 of potential, the sphere possesses \^__^-^ 

unit capacity. The capacities of spheres Fig. 148. 

{isolated in air) are proportional to their 
radii. We may imagine the charge q (Fig. 148) being 
brought nearer and nearer the sphere until it reaches the 
surface, then r becomes the radius of the sphere. We 
may further ijnagine the surface completely covered 
with little quantities q, so as to have a total charge Q 
uniformly distributed. Each little quantity would give 
to the sphere a potential q/r; the total potential of the 
sphere due to the charge Q on its surface would be Q/r. 
The greater the sphere the less would be the potential 
at any point in it due to the same charge Q. Thus it 
would be necessary to give a charge of 100 units to a 
sphere of 100 centimetres' radius in order to raise its 
potential to unity. It therefore has a capacity of 100. 
The earth has a capacity of about 630 millions (in electro- 
static units).* It is almost impossible to calculate the 
capacities of conductors of other shapes. It must be noted 
* Or about 700 microfarads (see Art. 283). 



258 ELECTRICITY AXD :^IAGXETISM part ii 

that the capacity of a sphere, as given above, means its 
capacity when far removed from other conductors or 
charges of electricity. The capacity of a conductor is 
increased by bringing near it a charge of an opposite kind; 
for the potential at the surface of the conductor is the sum 
of the potential due to its own charge, and of the potential 
of opposite sign due to the neighbouring charge. Hence, 
to bring np the resultant potential to unity, a larger 
quantity of electricity must be given to it ; or, in other 
words, its capacity is greater. This is the true way of 
regarding the action of Leyden jars and other condensers, 
and must be remembered by the student when he advances 
to the consideration of the theorv of condenser action, in 
Lesson XXIII. 

273. Surface-Density.* — Coulomb applied this term 
to denote the amount of electrification per unit of area 
at any point of a surface. It was mentioned in Lesson 
IT. that a charge of electricity was never distributed 
uniformly over a conductor, except in the case of an 
insulated sphere. Where the distribution is unequal, the 
density at any point of the surface may be expressed by 
considering the quantity of electricity which exists upon 
a smaU. unit of area at that point. If Q be the quantity 
of electricity on the small surface, and S be the area of 
that small surface, then the surface-density (denoted by 
the Greek letter p) will be given bv the equation, 

* The word Tension is sometimes used for that -vrliich is here precisely 
defined as Coulomb defined it. The term tension is, however, unfortunate ; 
and it is so often misapplied in text-books to mean not only surface- 
density but also potential, and eren electric force {i.e. the mechanical 
force exerted upon a material body by electricity\ that we might well 
avoid its use altogether. The term would be invaluable if we might 
adopt it to denote only the mechanical stress across a dielectric, as in Art. 
•279. This was Maxwell's use of the word, denoting a pulling force dis- 
tributed over an area, just as the word pressure means a distributed 
pushing force. 



CHAP. IV SUEFACE DENSITY OF CHAKGES 259 

la dry air, the limit to the possible electrification is 
reached when the density reaches the value of about 20 
units of electricity per square centimetre. If charged to 
a higher degree than this, the electricity escapes in 
" sparks " and " brushes " into the air. In the case of 
uniform distribution over a surface (as with the sphere, 
and as approximately obtained on a flat disk by a par- 
ticular device known as a guard-ring), the density is 
found by dividing the whole quantity of the charge by 
the whole surface. 

274. Surface-Density on a Sphere. — The surface 
of a sphere whose radius is r, is ^rrr^. Hence, if a 
charge Q be imparted to a sphere of radius r, the surface- 
density all over will be p = \ or, if we know the 

surface-density, the quantity of the charge will be 
Q = 47rrV 

The surface-density on two spheres joined by a thin 
wire is an important case. If the spheres are unequal, 
they will share the charge in proportion to their capacities 
(see Art. 40), that is, in proportion to their radii. If the 
spheres are of radii 2 and 1, the ratio of their charges 
will also be as 2 to 1. But their respective densities will 
be found by dividing the quantities of electricity on each 
by their respective surfaces. But the surfaces are pro- 
portional to the squares of the radii, i.e. as 4:1; hence, 
the densities will be as 1 : 2, or inversely as the radii. 
Xow, if one of these spheres be very small — no bigger 
than a point — the density on it will be relatively 
immensely great, so great that the air particles in 
contact with it will rapidly carry off the charge by 
convexion. This explains the action of points in dis- 
charging conductors, noticed in Cha^Dter I., Arts. 38, 45, 
and 47. 

275. Electric Images — It can be shown mathe- 
matically that if -f- ^ units of electricity are placed at a 
point near a non-insulated conducting sphere of radius 



260 ELECTRICITY AND MAGNETISM part ii 

r, at a distance d from its centre, the negative induced 
charge will be equal to — qr/d, and will be distributed 
over the nearest part of the surface of the sphere with a 
surface-density inversely proportional to the cube of the 
distance from that point. Lord Kelvin pointed out that, 
so far as all external points are concerned, the potential 
due to this peculiar distribution on the surface would 
be exactly the same as if this negative charge were all 
collected at an internal point at a distance of r — r'^/d 
behind the surface. Such a point may be regarded as a 
virtual image of the external point, in the same way as in 
optics we regard certain points behind mirrors as the 
virtual images of the external points from which the rays 
proceed. Clerk Maxwell has given the following defini- 
tion of an Electric Image : — An electric image is an 
electrified point, or system of points, on one side of a surface^ 
which would produce on the other side of that surface the 
same electrical action lohich the actual electrification of that 
surface really does produce. If the sphere is not connected 
to earth, and were unelectrified before + q was brought 
near it, we may find the surface- density at any point by the 
following convention. Imagine that there are coexisting 
on the sphere two charges, — rq/d and + rq/d respec- 
tively, the first being distributed so that its surface-density 
is inversely proportional to the cube of the distance from 
the electrified point, and the second being uniformly 
distributed. The actual surface-density is the algebraic 
sum of these two. A -1- charge of electricity placed I 
inch in front of a flat metallic plate induces on it a nega- 
tive charge distributed over the neighbouring region of 
the plate (with a density varying inversely as the cube 
of the distance from the point) ; but the electrical action 
of this distribution, so far as all points in front of the 
plate are concerned, would be precisely represented by 
its " image," namely, by an equal quantity of nega- 
tive electricity placed at a point 1 inch behind the 
plate. Many beautiful mathematical applications of this 



CHAP. IT EOUCE NEAR CHARGED SPHERE 261 

method have been made, enabling the distribution to be 
calculated in difficult cases, as, for example, the distri- 
bution of the charge on the inner surface of a hollow 
bowl. 

276. Force near a Charged Sphere. — It was shown 
above that the quantity of electricity Q upon a sphere 
charged until its surface-density was p, was 

Q = 47rr2p. 
The problem is to find the force exercised by this 
charge upon a + unit of electricity, placed at a point 
infinitely near the surface of the sphere. The charge on 
the sphere acts as if at its centre. The distance between 
the two quantities is therefore r. By Coulomb's Law the 

„ . Qxl iirr^p . 

force f = -—^ = -^ = 47rp. 

This important result may be stated in words as 
follows : — The force (in dynes) exerted Tjy a charged sphere 
upon a unit of electricity/ placed injinitely near to its surface, 
is numerically equal to 47r times the surface-density of the 
charge. 

277. Force near a Charged Plate of indefinite size. — 
Suppose a plate of indefinite extent to be charged so 
that it has a surface-density p. This surface-density 
will be uniform, for the edges of the plate are supposed 
to be so far off as to exercise no influence. It can be 
shown that the force exerted hy such a plate upon a -\- 
unit anywhere near it, luill he expressed (in dynes) numeri- 
cally as 27rp. This wiU be of opposite signs on opposite 
sides of the plate, being -f 27rp on one side, and — 27rp 
on the other side, since in one case the force tends to 
move the unit from right to left, in the other from left 
to right. It is to be observed, therefore, that the force 
changes its value by the amount of 47rp as the point 
passes through the surface. The same was true of the 
charged sphere, where the force outside was 47rp, and 
inside was zero. The same is true of all charged sur- 



262 ELECTRICITY AND MAGNETISM part ii 

faces. These two propositions are of the utmost impor- 
tance in the theory of Electrostatics. 

278, Proof of Theorem. — The elementary geometri- 
cal proof is as follows : — 

Required the Electric Force at point at any distance from a 

plane of infinite extent charged to surface-density p. 

Let P be the point, and PX or a the normal to the plane. 

Take any small cone having its apex at P. Let the solid angle 

of this cone be w ; let its length be r ; and e the angle its axis 




Fig. U9. 

makes with o. The cone meets the surface of the plane obliquely, 

and if an orthogonal section be made where it meets the plane, 

the angle between these sections will be = 6. 

, „ .^. orthosonal area of section 
Now solid angle w is by definition = ^= 

Hence, area of oblique section = r^w X 



charge on oblique section 



cos e' 



Hence if a + unit of electricity were placed at P, the force 

exerted on this by this small change = — ^^ X 1 -^- r2, 
•^ '^ cos 

or = -. 

cos e 

Resolve this force into two parts, one acting along the plane, 
the other along a, normal to the plane. The normal component 

along a is cos e x -^- =wp. 

° COS0 



CHAP. IT ELECTRIC STRESS IN MEDIUM 263 



But the whole surface of the plane may be similarly mapped 
out into small surfaces, all forming small cones, with their sum- 
mits at P. If we take an infinite number of such small cones 
meeting every part, and resolve their forces in a similar way, 
we shall find that the components along the plane will neutral- 
ize one another all round, while the normal components, or the 
resolved forces along a, will be equal to the sum of all their solid 
angles multiplied by the surface-density ; or 

Total resultant force along a — Sop. 

But the total solid angle subtended by an indefinite plane at 
a point is 2-, for it subtends a whole hemisphere. 

. • . Total resultant force = 27rp. 

279. Electric Stress in Medium. — In every electric 
field (Art. 13) there exists a tension along the lines of 
electric force accompanied by an equal pressure in all 
directions at .right angles to the lines. If F stands for 
the resultant electric force on a -f unit placed at any 
point in the field (i.e. the " electromotive intensity " at 
that point), the tension will be equal to F^/Stt (dynes per 
square centimetre). In media having dielectric capacities 
gTeater than unity the tension is proportionately greater. 
For the optical effects of these stresses see Art. 525. 



NOTE ON FUNDAMENTAL AND DERIVED UNITS 

280, Fundamental Units. —All physical qualities, such as 
force, velocity, etc., can be expressed in terms of the three 
fundamental quantities : length, mass, and time. Each of these 
quantities must be measured in terms of its own units. 

The system of units, adopted by almost universal consent, 
and used throughout these lessons, is the so-called "Centi- 
metre-Gramme-Second " system, in which the fundamental 
units are : — 

The Centimetre as a imit of length ; 

The Gramme as a unit of mass ; 

The Second as a unit of time. 

The Centimetre is equal to 0-3937 inch in length, and nomi- 



264 ELECTRICITY AND MAGNETISM part ii 



nally represents oue thousand-millionth part, or i qoq qqq qqq of a 
quadrant of the earth. 

The Metre is 100 centimetres, or 39'37 inches. 

The Kilometre is 1000 metres, or about 1093-6 yards. 

The Millimetre is jV of a centimetre, or 0-03937 inch. 

The Gramme represents the mass of a cubic centimetre of 
water at iPC, this is equal to 15-432 grains : the Kilogramme is 
1000 grammes or about 2-2 pounds. ^ 

281. Derived Units.— 

Area. — The unit of area is the square centimetre. 

Volume. — The unit of volume is the cubic centimetre. 

Velocity, — The unit of velocity is the velocity of a body 
which moves through unit distance in unit time, or the 
velocity of one centimetre per second. 

Acceleration: — The unit of acceleration is that acceleration 
which imparts unit velocity to a body in unit time, or 
an acceleration of one centimetre-per-second per second. 
The acceleration due to gravity imparts in one second a 
velocity considerably greater than this, for the velocity 
it imparts to falling bodies is about 981 centimetres per 
second (or about 32*2 feet per second) . The value differs 
slightly in different latitudes. At Greenwich the value 
of the acceleration of gravity is g = 981-1 ; at the Equa- 
tor g = 978-1 ; at the North Pole V = 983-1. 

Force. — The unit of force is that force which, acting for one 
second on a mass of oue gramme, gives .to it a velocity 
of one centimetre per second. It is called one Dyne. 
The force with which the earth attracts any mass is 
usually called the " weight " of that mass, and its value 
obviously differs at different points of the earth's sur- 
face. The force with which a body gravitates, i.e. its 
weight (in dynes), is found by multiplying its mass (in 
grammes) by the value of g at the particular place where 
the force is exerted. One pound force in England is 
about 445,000 dynes. 

Work. — The unit of work is the work done in overcoming 
unit force through unit distance, i.e. in pushing a body 
through a distance of one centimetre against a force of 
one dyne. It is called one jErf/. Since the " weight " of 
one gramme is 1x981 or 981 dynes, the work of raising 
one gramme through the height of one centimetre against 
the force of gravity is 981 ergs. 

Energy. — The unit of energy is also the erg ; for the energy 
of a body is measured by the work it can do. 



ELECTROSTATIC UNITS 265 



Heat. — The unit of heat, the calorie, is the amount of heat 
required to warm one gramme mass of water from 0° to 
1° (C.) ; and the dynamical equivalent of this amount of 
heat is 42 million ergs, which is the value of Joule's equi- 
valent, as expressed in C.G.S. measure (see also Art. 439) . 

These units are sometimes called "absolute" units; the 
term absolute, introduced by Gauss, meaning that they are 
independent of the size of any particular instrument, or of the 
value of gravity at any particular place, or of any other arbi- 
trary quantities than the three standards of length, mass, and 
time. It is, however, preferable to refer to them by the more 
appropriate name of " C.G.S. units," as being derived from the 
centimetre, the gramme, and the second. 

282. Electrical Units. — There are two systems of electrical 
units derived from the fundamental "C.G.S." units, one set 
being based upon the force exerted between two quantities of 
electricity, and the other upon the force exerted between two 
magnet poles. The former set are termed electrostatic units, the 
latter electro-magnetic units. The important relation between 
the two sets is explained in the note at the end of Chapter VI. 

283. Electrostatic Units. — No special names have been 
assigned to the electrostatic units of Quantity, Potential, 
Capacity, etc. The reasons for adopting the following values 
as units are given either in Chapter I. or in the present chapter. 

U7iit of Quantity. — The unit of quantity is that quantity 
of electricity which, when placed at a distance of one 
centimetre (in air) from a similar and equal quantity, 
repels it with a force of one dyne (Art. 2G2). 

Potential. — Potential being measured by ivork done in mov- 
ing a unit of + electricity against the electric forces, the 
unit of potential will be measured by the unit of work, 
the erg. 

Unit Difference of Potential. — Unit difference of potential 
exists between two points, when it requires the expendi- 
ture of one erg of work to bring a -{- unit of electricity 
from one point to the other against the electric force 
(Art. 265) . 

Unit of Capacity. — That conductor possesses unit capacity 
which requires a charge of one unit of electricity to 
bring it up to unit potential. A sphere of one centi- 
metre radius possesses unit capacity (Art. 272). 

Specific Inductive Capacity, or Dielectric Coefficient, is de- 
fined in Art. 295 as the ratio between two quantities of 
electricity. The specific inductive capacity of the air 



266 ELECTRICITY AND MAGNETISM part ii 



is, in the absence of any knowledge of its absolute 
value, taken as unity. 
Electromotive Intensity is the electric force or intensity of an 
electric field at any point, and is measured by the force 
which it exerts on a unit charge placed at that point. 

It may be coiiYeiiient here to append the rules for re- 
ducing to then- corresponding values in terms of the prac- 
tical (electro-magnetic) units values that may have been 
expressed in terms of the electrostatic units, as follows : — 

Potential. To bring to volts multiply by 300. 
Capacity. To bring to microfarads divide by 900,000. 
Quantity. To bring to coulombs divide by 3 X 109. 
Current. To bring to amperes divide by 3 x 10^. 
Resistance. To bring to ohms multiply by 9 X lO^i. 
Example. — Suppose two equally charged spheres whose centres are 
40 centimetres apart are found to repel one another with a force 
of 630 dynes (= about the Aveight of 10 grains). By the law of 
inverse squares we find that the charge on each is 1004 (electro- 
static units. Dividing by 3 x 10^ we find that this amounts to 
0-0000003347 coulomb. 

284. Dimensions of Units. — It has been assumed above 
that a velocity can be expressed in centimetres per second ; for 
velocity is rate of change of place, and it is clear that if change 
of place may be measured as a length in centimetres, the rate 
of change of place will be measured by the number of centi- 
metres through which the bodj' moves in unit of time. It is 
impossible, indeed, to express a velocity without regarding it as 
the quotient of a certain number of uuits of length divided by 
a certain number of units of time. In other words, a velocity 
_ a length 
— ~^|~time~ ' *^^' ^*^^optiiis L as a symbol for length, and T as a 

symbol for time, V = -, which is still more conveniently written 

V = L X T -1. In a similar way acceleration being rate of 

change of velocitv, we have A = - = = —z = 'LxT--. 

T TXT t2 

Now these physical quantities, " velocity " and " acceleration," 
are respectively always quantities of the same nature, no matter 
whether tlie centimetre, or the inch, or the mile, be taken as the 
unit of length, or the second or any other interval be taken as 
the unit of time. Hence we say that these abstract equations 
express the dimensions of those quantities with respect to the 
fundamental quantities length and time. A little consideration 



DIMENSIONS OF UNITS 



267 



Trill sho\v the student that the dimensions of the various units 
mentioned above will therefore be as given in the table below. 

The dimensions of magnetic units are given in the Table in 
Art. 35(3, p. 348. 

Table of Dimensions of Units. 





UXITS. 


Dimensions. 


I 

m 
t 


(^Fundamental) 
Length 
Mass 
Time 


L 
M 
T 


V 

a 
f 


{Derived) 
Area = L x L = 
Volume = L X L X L = 
Telocity = L-^T = 
Acceleration = velocity -^ time = 
Force = mass x acceleration = 
■Work = force x length = 


L2 

L3 

LT-^ 

LT-^ 

MLT-' 

ML2T"^ 


i 

T 
E 

C 
Tc 
F 


{Electrostatic) 


m^tJt-^ 
MUiT-=^ 

L-iTi 
L 

a numeral 


Quantity =^lbrce x(distance)2 = 
Current = quantity -^ time = 
Potential = work 4- quantity = 
Resistance = potential -4- current = 
Capacity = quantity -=- potential = 
Sp. Ind. Capacity = quantity -=- another quantity 
Electromotive Intensity = force -^ quantity = 



Lesson XXII. — Electrometers 

285. In Lesson IL we described a number of electro- 
scopes or instruments for indicating the presence and 
sign of a charge of electricity ; some of these also served 



268 ELECTRICITY AND MAGNETISM part ii 

to indicate roughly the amount of these charges, but 
none of them save the torsion balance could be regarded 
as affording an accurate means of measm-ing either the 
quantity or the potential of a given charge. An instru- 
ment for measuring differences of electrostatic potential is 
termed an Electrometer. Such instruments can also be 
used to measure electric quantity indirectly, for the 
quantity of a charge can be ascertained by measuring 
the potential to which it can raise a conductor of knovni 
capacity. The earliest electrometers attempted to meas- 
ure the quantities directly. Lane and Snow Harris 
constructed " Unit Jars " or small Leyden jars, which, 
in order to measure out a certain quantity of electri- 
city, were charged and discharged a certain number of 
times. 

286. Repulsion Electrometers. — The torsion balance, 
described in Art. 18, measures quantities by measuring 
the forces exerted by the charges given to the fixed and 
movable balls. It can only be applied to the measure- 
ment of repelling forces, for the equilibrium is unstable 
in the case of a force of attraction. 

Beside the gold-leaf electroscope and others described 
in Lesson IL, there exist several finer electrometers based 
upon the principle of repulsion, some of which resemble 
the torsion balance in having a movable arm turning 
about a central axis. Amongst these are the electrometers 
of Dellmann and of Peltier. In the latter a light arm 
of aluminium, balanced upon a point, carries also a small 
magnet to direct it in the magnetic meridian. A fixed 
arm, in metallic contact with the movable one, also lies 
in the magnetic meridian. A charge imparted to this 
instrument produces a repulsion between the fixed and 
movable arms, causing an angular deviation. Here, how- 
ever, the force is measured not by being pitted against 
the torsion of an elastic fibre, or against gravitation, but 
against the directive magnetic force of the earth acting 
on the small needle. Now this depends on the intensity 



CHAP. IT ELECTROMETERS 269 

of the horizontal component of the earth's magnetism 
at the place, on the magnetic moment of the needle, 
and on the sine of the angle of its deviation. Hence, 
to obtain qnantitative values for the readings of this 
electrometer, it is necessary to make preliminary experi- 
ments and to " calibrate " the degree-readings of the 
deviation. 

287. Attracted - Disk Electrometers. — Snow Harris 
was the first to construct an electrometer for measur- 
ing the attraction between an electrified and a non- 
electrified disk ; and the instrument he devised may 
be roughly described as a balance for weigliing a charge 
of electricity. More accurately speaking,' it was an in- 
strument resembling a balance in form, carrying at one 
end a light scale pan; at the other a disk was hung 
above a fixed insulated disk, to which the charge to be 
measured Avas imparted. The chief defect of this instru- 
ment was the irregular distribution of the charge on the 
disk. The force exerted by an electrified point falls off 
inversely as the square of the distance, since the lines 
of force emanate in radial lines. But in the case of a 
uniformly electrified plane surface, the lines of force are 
normal to the surface, and parallel to one another ; and 
the force is independent of the distance. The distribu- 
tion over a small sphere nearly fulfils the first of these 
conditions. The distribution over a flat disk would 
nearly fulfil the latter condition, were it not for the 
perturbing effect of the edges of the disk where the 
surface -density is much greater (see Art. 38); for 
this reason Snow Harris's electrometer was very im- 
perfect. 

Lord Kelvin introduced several very important modifi- 
cations into the construction of attracted-disk electro- 
meters, the chief of these being the employment of the 
" guard-plate " and the providing of means for work- 
ing with a definite standard of potential. It would be 
beyond the scope of these lessons to give a complete 



270 



ELECTRICITY AND MAGNETISM part ii 



description of all the various forms of attracted-disk 
electrometer ; * but the main princi]Dles of them all can 
be readily explained. 

The disk C, whose attraction is to be measured, is 
suspended (Fig. 150) within a fixed guard-plate B, which 
surrounds it without touching it, and which is placed in 
metallic contact with it by a fine wire. A Lever L 
supports the disk, and is furnished with a counterpoise. 
In order to know whether the disk is precisely level with 
the lower surface of the guard-plate a little gauge or index 




Fig. 150. 

is fixed above, and provided with a lens I to observe its 
indications. Beneath the disk and guard-plate is a second 
disk A, supported on an insulating stand. This lower 
disk can be raised or lowered at will by a micrometer 
screw, great care being taken in the mechanical arrange- 
ments that it shall always be parallel to the plane of the 
guard-plate. Xow, since the disk and guard-plate are in 
metallic connexion with one another, they form virtually 
part of one surface, and as the irregularities of distribution 

* For these the student is referred to the volume of Lord Kelvin's 
papers, " On Electrostatics and Magnetism " ; or to Professor Andrew 
Gray's Absolute Measurements in Electricity and Magnetism. 



CHAP. IT ATTRACTED-DISK ELECTROMETERS 271 

occiu' at the edges of the surface, the distribution over the 
area of the disk is practically uniform. Any attraction of 
the lower plate upon the disk might be balanced either by 
increasing the weight of the counterpoise, or by putting a 
torsion on the aluminium wire which serves as a fulcrum ; 
but in practice it is found most convenient to obtain a 
balance by altering the distance of the lower plate until 
the electric force of attraction exactly balances the forces 
(whether of torsion or of gravity acting on the counter- 
poise) which tend to lift the disk above the level of the 
guard-plate. 

The theory of the instrument is simple also. Let V^ 
represent the potential of the movable disk, which has a 
positive charge of surface-density p, and let Vg be the 
potential of the fixed plate, upon which is a charge 
of surface-density — p. The difference of potential 
Vj — Yg is the work which would have to be done upon 
a unit of positive charge in taking it from Vg to V^. 
Now the force upon such a unit placed between the two 
plates would be (an attraction of 2 irp due to the fixed 
plate, and a repulsion of 2 irp due to the movable plate, 
see Art. 278) altogether 4 7rp, and if the distance between 
the plates were D. Work = force x distance. 

V^- V2 = 47rpD. 

If S is the area of the movable plate, Sp is the total 
quantity of electricity on it ; therefore it would be 
attracted by the fixed plate with a force F = 2 7rp x Sp. 
From this we get 

Substituting this value of p in the above equation, we get 

If F is measured in dynes, S in square centimetres, and 
D in centimetres, the potentials will be in absolute electro- 



272 ELECTRICITY A^^D MAGNETISM part ii 

static units, and must be multiplied by 300 to bring to 
volts (see Art. 283). 

From this we gather that, if the force F remains the 
same throughout the experiments, the difference of poten- 
tials between the disks will he simply proportional to the dis- 
tance between them when the disk is in level equilibrium. 

And the quantity \— ^ niay be determined once for 

all as a " constant " of the instrument. 

In the more elaborate forms of the instrument, such 
as the " absolute electrometer," and the " portable 
electrometer," the disk and guard-plate are covered 
with a metallic cage, and are together placed in com- 
munication with a condenser to keep them at a known 
potential. This obviates having to make measurements 
with zero readings, for the differences of potential will 
now be proportional to differences of micrometer readings^ 



Y, - Y, = (D, - D,) -yj^. 

The condenser is provided in these instruments with 
a gauge, itself an attracted disk, to indicate when it is 
charged to the right potential, and with a replenisher to 
increase or decrease the charge, the replenisher being a 
little influence machine (see Art. 50). 

288. The Quadrant Electrometer. — The Quadi-ant 
Elecfcrometer of Sir W. Thomson is an example of a 
different class of electrometers, in which use is made of 
an auxiliary charge of electricity previously imparted to 
the needle of the instrument. The needle, which con- 
sists of a thin flat piece of aluminium hung horizontally 
by a fibre of thin wire, thus charged, say positively, will 
be attracted by a — charge, but repelled by a -f charge. 
Such attraction or repulsion will be stronger in proportion 
to these charges, and in proportion to the charge on the 
needle. Four quadrant-pieces (Fig. 151) of brass are fixed 



CHAP. IV QUADRANT ELECTROMETER 273 

horizontally below the needle without touching it or one 
another. Opposite quadrants are joined with fine wires. 
If quadrants 1 and 3 are ever so little + as compared 
with quadrants 2 and 4, the needle will turn away from 
the former to a position more nearly over the latter. 

If there is the slightest difference of potential between 
the pairs of quadrants, the needle, which is held in its 
zero position by the elasticity of the 
wire, will turn, and so indicate the 
difference of potential. AVhen these 
deflexions are small, the scale readings 
will be very nearly proportional to the 
difference of potential. The instru- 
ment is sufficiently delicate to show a 
difference of potential between the 
quadrants as small as the y^ of that 
of the Daniell's cell. If V^^ be the potential of one pair of 
quadrants, Y^ that of the other pair, and Vo the potential 
of the needle, the force tending to turn will be proportional 
to Vj — Yg, and will also be proportional to the difference 
between Vg and the average of V^ and Vg. Or, in 
symbols, 




f=a(V,-Y,) {y. 



where a is a constant depending on the construction of 
the particular instrument. 

Fig. 152 shows a very simple form of the Quadrant 
Electrometer, as arranged for qualitative experiments. 
The four quadrants are enclosed within a glass case, and 
the needle, which carries a light mirror M below it, is 
suspended from a torsion head C by a very thin metallic 
wire F. It is electrified to a certain potential by being- 
connected, through a wire attached to C, with a charged 
Leyden jar or other condenser. In order to observe the 
minutest motions of the needle, a reading-telescope and 
scale are so placed that the observer looking through the 

T 



274 



ELECTRICITY AND MAGNETISM part ii 



telescope sees an image of the zero of the scale reflected 
in the little mirror. The wires connecting quadrants 1 
and 3, 2 and 4, are seen above the top of the case. 

For very exact measurements many additional refi^ne- 
ments are introduced into the instrument. Two sets of 
quadrants are employed, an upper and a lower, having 
the needle between them. The torsion wire is replaced 
by a delicate bifilar suspension (Art. 130). 
To keep up the charge of the Ley den jar a 
"replenisher " is added; and an ''attracted- 
disk," like that of the Absolute Electro- 
meter, is employed in order to act as a 
gauge to indicate when the jar is charged 
to the right potential. In these forms the 
jar consists of a glass vessel placed below 
the quadrants, coated extern all}^ wdth strips 
of tinfoil, and containing strong sulphuric 
acid, which serves the double function of 




Fig. 152. 



keeping the apparatus dry by absorbing the moisture 
and of acting as an internal coating for the jar. It is 
also more usual to throw a spot of light from a lamp 
upon a scale by means of the little mirror (as described in 
the case of the Mirror Galvanometer, in Art. 21.5), than 
to adopt the subjective method with the telescope, which 
only one person at a time can use. When the instrument 
is provided with replenisher and gauge, the measurements 



CHAP. IV ELECTROSTATIC VOLTMETER 275 

can be made in terms of absolute units, provided the " con- 
stant " of the particular instrument (depending on the 
suspension of the needle, size and position of needle and 
quadrants, potential of the gauge, etc.) is once ascertained. 

289. Use of Quadrant Electrometer. — An example will 
illustrate the mode of using the instrument. It is known that 
when the two ends of a thin wire are kept at two different 
potentials a current flows through the wire, and that if the 
potential is measured at different points along the wire, it is 
found to fall off in a perfectly uniform manner from the end 
that is at a high potential down to that at the low potential. At 
a point one quarter along the potential will have fallen off one 
quarter of the whole difference. This could be proved by join- 
ing the two ends of the wire through which the current was 
flowing to the terminals of the Quadrant Electrometer, when one 
pair of quadrants would be at the high potential and the other 
at the low potential. The needle would turn and indicate a cer- 
tain deflexion. Now, disconnect one of the pairs of quadrants 
from the low potential end of the wire, and place them in com- 
munication with a point one quarter along the wire from the 
high potential end. The needle will at once indicate that the 
difference of potential is but one quarter of what it was before. 

Often the Quadrant Electrometer is employed simply as a 
very delicate electrosco/^e in systems of measurement in which 
a difference of electric potential is measured by being balanced 
against an equal and opposite difference of potential, exact bal- 
ance being indicated by there being no deflexion of the Electro- 
meter needle. Such methods of experimenting are known as 
Null Methods, or Zero Methods. 

290. Electrostatic Voltmeter. — We have seen that 
in the quadrant electrometer it is necessary to give the 
needle a high initial charge, the reason being that if 
there did not exist between the quadrants and the needle 
a much greater difference of potential than the small 
voltage we are measuring, the force tending to turn the 
needle would be too small to be conveniently observed. 
Where, however, \ve are dealing with high differences of 
potential a separately-charged needle is not requisite ; 
we may simply join one conductor to the needle and 
the other to a set of quadrants, and the force of 



276 



ELECTRICITY AND MAGNETISM part ii 




attraction, ^vhich, other things being equal, increases as 
the square of the difference of potential, is sufficiently 
great to give reliable readings. This 
is known as the idiostatic method of 
using the instrument. 

A front view of the instrument as 
commonly used to measm'e differences 
of potential of 1000 volts or more, is 
shown in Fig. 153. The needle NX 
is a paddle-shaped plate of aluminium 
supported by knife edges at its centre ; 
its position is controlled by gravity, 
little weights being hung on a projec- 
tion at its lower end. The quadrants 
Q are both behind and in front of it, 
and so placed that when a difference 
of potential exists between the needle and them the 
needle is deflected from its normal position and moves 
its pointer over a graduated scale. 

It will be seen that it does not matter whether the 
needle is jDositively charged and the 
quadrants negatively charged or rice 
versa: an attraction between the two 
will alw^ays take place, so a deflexion 
w^ill be given even when the differ- 
ence of potential is rapidly alternat- 
ing. This property of the instrument 
makes it exceedingly useful for the 
measurement of voltage when alter- 
natuig currents are used. 

Another advantage of this instru- 
ment over the high-resistance galva- 
nometers that are used as voltmeters is, 
that it does not take any current, and con- 
sequently it does not waste any power. 

In order to make the electrostatic voltmeter sufficiently 
delicate to measure down to 100 volts or so, a number of 




CHAP. IV CAPACITY OF CONDENSERS 277 

needles is placed horizontally one above the other on 
a vertical aluminium wire, and attracted by a tier of 
quadrants symmetrically placed on each side ; this instru- 
ment is Lord Kelvin's multicellular voltmeter. It is shown 
in elevation and plan in Fig. 154. 

291. Dry-Pile Electrometer. — The principle of sym- 
metry observed in the Quadrant Electrometer was pre- 
viously employed in the Electroscope of Bohnenberger 
— a much less accurate instrument — in which the charge 
to be examined was imparted to a single gold leaf, placed 
symmetrically between the poles of a dry-pile (Art. 193) 
tow^ard one or other pole of which the leaf was attracted. 
Fechner modified the instrument by connecting the + 
pole of the dry-pile with a gold leaf hanging between 
two metal disks, from the more + of which it was re- 
pelled. The inconstancy of dry-piles as sources of electri- 
fication led Hankel to substitute a battery of a very large 
number of small Daniell's cells. 

292. Capillary Electrometers. — The Capillary Elec- 
trometer of Lippmann, as modified by Dewar, was de- 
scribed in Art. 253. 



Lesson XXm. — Dielectric Capacity, etc. 

293. A Leyden jar or other condenser may be 
regarded as a conductor, in which (owing to the particu- 
lar device of bringing near together the two oppositely- 
charged surfaces) the conducting surface can be made to 
hold a very large charge without its potential (whether 
-f or — ) rising very high. The capacity of a condenser, 
like that of a simple conductor, will be measured (see 
Art. 271) by the quantity of electricity required to pro- 
duce unit rise of potential. 

294. Theory of Spherical Condenser. — Suppose a 
Leyden jar made of two concentric metal spheres, one 
inside the other, the space between them being filled 



278 



ELECTRICITY AND MAGNETISM part ii 



by air. The inner one, A, will rej)resent the interior 
coating of tinfoil, and the 
outer sphere, B (Fig. 155), will 
represent the exterior coating. 
Let the radii of these spheres 
be r and r' respectively. Sup- 
pose a charge of Q units to be 
imparted to A ; it will induce 
on the inner side of B an equal 
negative charge — Q, and to 
the outer side of B a charge 
+ Q will be repelled. This 
latter is removed by contact 
with " earth," and need be no 
further considered. The po- 
tential * at the centre M, calculated by the rule given in 
Art. 263, will be 




Vm = - - 



Q Q 



At a point ^N", outside the outer sphere and quite near to 
it, the potential will be the same as if these two charges, 
+ Q and — Q, were both concentrated at M. Hence 



So then the difference of potentials will be 
Q 



^ M — ^N 



Q 



^) 



whence 



Q 



But by Art. 270 the capacity K 



Q 



V, 



therefore 



K 



* The student must remember that as there is no electric force within 
a closed conductor, the potential at the middle is just the same as at any 
other point inside. 



INDUCTIVITY 279 



We see from this formula that the capacity of the 
condenser is proportional to the size of the metal globes, 
and that if the insulating layer is very thin, — that is, if 
}• be very nearly as great as r', r' — r will become very 

small, and the value of the expression —LL^ will become 

r' — r 
YQYy great ; which proves the statement that the capacity 
of a condenser depends upon the tliinness of the layer 
of dielectric. If r' is very great compared wdth r, the 
expression for the capacity becomes equal simply to r, 
that of the inner sphere wdien isolated. 

295. Specific Inductive Capacity. — Cavendish was 
the Jirst to discover that the capacity of a condenser 
depended not on its actual dimensions only, but upon the 
inductive power of the material used as the dielectric be- 
tween the two surfaces. If two condensers (of any of the 
forms to be described) are made of exactly the same size, 
and in one of them the dielectric be a layer of air, and 
in the other a layer of some other insulating substance, 
it is found that equal quantities of electricity imparted 
to them do not produce equal differences of potentials ; 
or, in other words, it is found that they have not the 
same capacity. If the dielectric be mica, for example, it 
is found that the capacity is about six times as great ; for 
mica possesses a high inductive power and allows the 
transmission across it of electrostatic influence six times 
as w^ell as air does. The name specific inductive capac- 
ity,* or dielectric capacity, is given to the ratio between 
the capacities of tw^o condensers equal in size, one of 
them being an air condenser, the other filled with the 
specified dielectric. The specific inductive capacity of 
dry air at the temperature 0° C, and pressure 76 cen- 
timetres, is taken as the standard, and, in the absence of 
any known way of finding its absolute value, is reckoned 

* The name is not a very happy one, — inductivity \\o\x\^ have been 
better, and is the analogous term, for dielectrics, to the term "conduc- 
tivity " used for conductors. The term dielectric coefficient is also used 
by some modern writers. 



280 



ELECTRICITY AND MAGNETISM part n 



as unity. The symbol k is used to denote the dielectric 
capacity of any material. 

Cavendish, about the year 1775, measured the dielec- 
tric capacity of glass, bees-wax, and other substances, by 
forming them into condensers between two circular metal 
plates, the capacity of these condensers being compared 
with that of an air condenser (resembling Fig. 42) and 
with other condensers which he 
called " trial-plates." He even 
went so far as to compare the 
capacities of these "trial-plates" 
"with that of an isolated sphere 
of 12 i inches diameter hung up 
in a room. 

296. Faraday's Experi- 
ments. — In 1837 Faraday, who 
did not know of the then 
unpublished researches of 
Cavendish, independently dis- 
covered specific inductive ca- 
pacity, and measured its value 
for several substances, using for 
this purpose two condensers of 
the form shown in Fig. 156. 
Each consisted of a brass ball A, 
enclosed inside a hollow sphere 
of brass B, and insulated by a 
long plug of shellac, up which 
passed a wire terminating in a 
knob a. The outer sphere con- 
sisted of two parts which could 
be separated from each other in order to fill the hollow 
space with any desired material : the experimental process 
then was to compare their capacities when one was 
filled with the substance to be examined, the other 
containing only dry air. One of the condensers was 
charged wdth electricity. It was then made to share its 




CHAP. IV DIELECTRIC CAPACITY 281 

charge "U'ith the other condenser, by pnttmg the two mner 
coatings into metallic commnnication with one another ; 
the outer coatings also being in commnnication with one 
another. If their capacities were equal they would share 
the charge equally, and the potential after contact would 
be just half what it was in the charged condenser before 
contact. If the capacity of one was greater than the 
other the final potential would not be exactly half the 
original potential, because they would not share the charge 
equally, but in proportion to their capacities. The po- 
tentials of the charges were measured before and after 
contact by means of a torsion balance.* Faraday's results 
showed the following values : Sulphur, 2-26 ; shellac, 2-0 ; 
glass, 1-76 or more. 

297. Recent Researches. — Since 1870 large addi- 
tions to our knowledge of this subject have been made. 
Gibson and Barclay measured the inductivity of paraffin 
wax by comparing the capacity of an air condenser 
with one of paraffin by means of an arrangement of slid- 
ing condensers, using a sensitive quadrant electrometer to 
adjust the capacity of the condensers exactly to equality. 
Hopkinson has examined the dielectric power of glass of 
various kinds, using a constant battery to produce the 
required difference of potentials, and a condenser provided 
with a guard-ring for a purpose similar to that of the 
guard-ring in absolute electrometers. Gordon made a 
large number of observations, using a delicate apparatus 
known as a statical " inductivity balance," which is a 
complicated condenser, so arranged in connexion with a 

* The value of the dielectric capacity k could then be calculated as 
follows : — 

Q = YK=Y'K + Y'K^- 

(where K is the capacity of the first apparatus and V its potential, and 
V the potential after communication with the second apparatus, whose 
capacity is K^) : hence 

V = V' (1 + A;), 

and h = — ^^^ — 



282 ELECTRICnr AND MAGNETISM part li 

quadrant electrometer that T^'hen the capacities of the 
separate parts are adjusted to equality there shall be no 
deflexion in the electrometer, whatever be the amount or 
sign of the electrification at the moment. This arrange- 
ment, when employed in conjunction with an induction 
coil (Fig. 135) and a rapid commutator, admits of the in- 
ductive capacity being measm^ed when the duration of 
the actual charge is only very small, the electrification 
being reversed 12,000 times per second. Such an instru- 
ment, therefore, overcomes one great difficulty besetting 
these measm-ements, namely, that owing to the apparent 
absorption of part of the charge by the dielectric (as 
mentioned in Art. 61), the capacity of the substance, 
when measured slowl}^, is different from its "instanta- 
neous capacity." This electric absorption is discussed 
further in Art. 299. For this reason the values assigned 
by different observers for the dielectric capacity of various 
substances differ to a most perplexing degree, especially 
in the case of the less perfect insulators. The following 
table summarizes Gordon's observations : — 

Air 1-00 

Glass 3-013 to 3'2o8 

Ebonite 2-284 

Guttapercha .... 2-i62 

Indiarubber .... 2-220 to 2-497 

Paraffin (solid) .... 1-9936 

Shellac 2-74 

Sulphur 2-58 

Hopkinson, whose method was a " slow " one, found 
for glass much higher inductive capacities, ranging from 
6-5 to 10-1, the denser kinds having higher capacities. 
Mica has values ranging from 5-5 to 8. Cavendish 
observed that the apparent capacity of glass became much 
greater at those temperatures at which it begins to con- 
duct electricity. Boltzmann has announced that in the 
case of two crystalline substances, Iceland spar and sul- 
phui-, the inductive capacity is different in different 



CHAP. IT 



INDUCTIVITY OF FLUIDS 



283 



directions, according to their position with respect to the 
axes of crystallization. 

298. Dielectric Capacity of Liquids and Gases. — 
The dielectric capacity of liquids also has specific values, 
as follows : — 



Turpentine 
Petroleum 
Bisulphide of Carbou 



2-16 

2-03 to 2-07 

1-81 



Faraday examined the inductive capacity of several 
gases by means of his apparatus (Fig. 156), one of the 
condensers being filled with air, the other with the gas 
which was let in through the tap below the sphere after 
exhaustion by an air pump. The method was too rough, 
however, to enable him to detect any difference between 
them. More recently Boltzmann, and independently 
Ayrton and Perry, have measured the dielectric capaci- 
ties of different gases by very exact methods ; and their 
results agree very fairly. 





Boltzmann. 


Ayrton and Perry. 


Air 


(1) 


(1) 


. Vacuum .... 


(0-999il0) 


(0-9985) 


Hydrogen .... 


0'999674: 


0-9998 


Carbonic Acid . 


1-000356 


1-0008 


defiant Gas 


1-000722 




Sulphur Dioxide 




1-0037 



The effect of using instead of air a medium of higher 
dielectric power k is to change the forces exerted between 
charged bodies. For given fixed charges the forces vary 
inversely as ^■; while for given differences of potential 
between the bodies the forces vary directly as k. 

299. Mechanical Effects of Dielectric Stress. — That 
different insulating substances have specific inductive 
power sufficiently disproves the idea that influence is 



284 . ELECTRICITY AND MAGNETISM part ii 

merely an " action at a distance," for it is evident that 
tlie dielectric medium is itself concerned in the propaga- 
tion of influence, and that some media allow influence to 
take place across them better than others. The existence 
of a residual charge (Art. 61) can be explained either on 
the supposition that the dielectric is composed of hetero- 
geneous particles which have unequal conducting powers, 
as Maxwell has suggested, or on the hypothesis that the 
molecules are actually subjected to a strain from which, 
especially if the stress be long-continued, they do not 
recover all at once. Kohlrausch and others have pointed 
out the analogy between this phenomenon and that of the 
" elastic recovery " of solid bodies after being subjected to 
a bending or a twisting strain. A fibre of glass, for 
example, twisted by a certain force, flies back when 
released to almost its original position, a slight sub-per- 
manent set remains, from which, however, it slowly 
recovers itself, the rate of its recovery depending upon 
the amount and duration of the original twisting strain. 
A quartz fibre never shows any sub-permanent set. Hop- 
kinson has shown that it is possible to superpose 
several residual charges, even charges of opposite signs, 
which apparently "soak out " as the strained material 
gradually recovers itself. Perry and Ayrton have also 
investigated the question, and have shown that the 
polarization charges in voltameters exhibit a similar 
recovery.* Air condensers exhibit no residual charges. 
Nor do plates of quartz cut from homogeneous crystal. 
When a condenser is discharged a sound is often 
heard. This was noticed by Lord Kelvin in the case 
of air condensers; Yarley and Dolbear have constructed 
telephones in which the rapid charge and discharge of 

* It ^yo^^ld appear, therefore, probable that Maxwell's suggestion of 
heterogeneity of structure, as leading to residual electrification at the 
bounding surface of the particles whose electric conductivities differ, is the 
true explanation of the "residual" charge. The phenomenon of elastic 
recovery may itself be due to heterogeneity of structure. Glass itself is a 
mixture of different silicates. 




Fiff. 157. 



CHAP. IV POLARIZATION OF DIELECTRIC 285 

a condenser gave rise to musical tones and to articulate 
speech. 

As to the precise nature of the molecular or mechanical 
operations in the dielectric Avhen thus subjected to the 
stress of electrostatic induction, nothing is known. One 
pregnant experiment of Faraday is of great importance, 
by showing that induction is, as he expressed it, " an 
action of contiguous particles." In a glass trough (Fig. 
157) is placed some oil of turpentine, in which are put 
some fibres of dry ^ 

silk cut into small p"- — i 

bits. Two wu-es 
pass into the 
liquid, one of 
which is joined 
to earthj the other 
being put into connexion with the collector of an 
electrical machine. The bits of silk come from all parts 
of the liquid and form a quivering chain of particles from 
^dre to wire, showing the electric lines of force. They 
at once disperse if the electric discharge is stopped. 
Faraday regarded this as typical of the internal actions 
in every case of influence across a dielectric, the particles 
of which he supposed to be " polarized," that is, to be 
turned into definite positions, each particle having a 
positive and a negative end. The student will perceive 
an obvious analogy, therefore, between the condition of 
the particles of a dielectric across which influence is 
taking place, and the molecules of a piece of iron or steel 
when subjected to magnetic induction. Instead of silk, 
crystals of sulphate of quinine may be used. Or finely- 
divided sulphide of antimony may be strewn on the 
bottom of a glass dish and covered with a layer of 
petroleum, to show the electric lines of force. 

Siemens has shown that the glass of a Ley den jar 
is sensibly warmed after being several times rapidly 
charged and discharged. This obviously implies that 



286 ELECTRICITY AND MAGNETISM part ii 

molecular movement accom.panies the changes of dielec- 
tric stress. 

300. Electric Expansion. — Fontana noticed that the 
internal volume of a Leyden jar increased when it was 
charged. Priestly and Volta sought to explain this by 
suggesting that the attraction between the two charged^ 
surfaces compressed the glass and caused it to expand 
lateral^. Duter showed that the amount of apparent 
expansion was inversely proportional to the thickness of 
the glass, and varied as the square of the potential differ- 
ence. Quincke has recently shown that though glass 
and some other insulators exhibit electrical expansion, 
an appareiit contraction is shown by resins and oily 
bodies under electrostatic stress. He connects with these 
properties the production of optical strain and of double 
refraction discovered by Kerr. (See Lesson on Electro- 
optics, Art. 525). 

301. Submarine Cables as Condensers. — A sub- 
marine telegraph cable may act as a condenser, the 
ocean forming the outer coating, the internal wire the 
inner coating, while the insulating layers of guttapercha 
serve as dielectric. When one end of a submerged cable 
is connected to, say, the + pole of a powerful battery, 
electricity flows into it. Before any signal can be 
received at the other end, enough electricity must flow 
in to charge the cable to a considerable potential, an 
operation which may in the case of long cables require 
some seconds. Faraday predicted that this retardation 
would occur. It is, in actual fact, a serious obstacle 
to rapid signalling through Atlantic and other cables. 
Professor Fleeming Jenkin has given the following ex- 
perimental demonstration of the matter. Let a mile of 
insulated cable wire be coiled up in a tub of water 
(Fig. 158), one end N being insulated. The other end 
is joined up through a long-coil galvanometer G to the 
+ pole of a large battery, whose — pole is joined by a 
wke to the water in the tub. Directly this is done, the 



CABLES AS CONDENSERS 



287 



needle of the galvanometer will show a violent deflexion, 
electricity rushing through it into the interior of the 
cable, and a — charge being accumulated on the outside of 
it where the water touches the guttapercha. For perhaps 
an hour the flow will go on, tliough diminishing, until the 
cable is fully charged. Xow remove the battery, and 
instead join up a and h hj a wire ; the charge in the 
cable will rush out through the galvanometer, which will 




Fig. 153. 

show an opposite deflexion, and the residual charge will 
continue "soaking out" for a long time- 
Long land-lines carried overhead also possess a measur- 
able capacity, and tend to retard the signals. 

302. Use of Condensers. — To obviate this retarda- 
tion and increase the speed of signalling in cables * several 
devices are adopted. Very delicate receiving instruments 
are used, requiring only a feeble current; for with the 
feebler batteries the actual charge given to the cable 
is less. In some cases a key is employed which, after 
every signal, immediately sends into the cable a charge 
of opposite sign, to sweep out, as it were, the charge left 
behind. Often a condenser of several microfarads' 
capacity is interposed in the circuit at each end of the 
cable to curb the signal, or make it shorter and sharper, 
and by its reaction assist the discharge. In duplex 

* The capacity of tlie "Direct" Atlantic cable from BaUinskelligs 
(Ireland) to Nova Scotia is 992 microfarads. 



288 ELECTRICITY AND MAGNETISM part ii 

signalling (Art. 503) the resistance and electrostatic capa- 
city of the cable have to be met by balancing against 
them an '' artificial cable " consisting of a wire of equal 
resistance, combined with a condenser of equal capacity. 
Messrs. Muirhead constructed for duplexing the Atlantic 
cable a condenser containing 100,000 square feet (over 
two acres of surface) of tinfoil. Condensers are also 
occasionally used on telegraph lines in single working to 
obviate disturbances from earth currents. They are con- 
structed by placing sheets of tinfoil between sheets of 
mica or of paraffined paper, alternate sheets of foil being 
connected together. The paper is the finest bank-w^ove, 
carefully selected to be free from minute holes. Two 
thicknesses, drawn through a bath of the purest paraffin 
wax heated till it melts, are laid between each foil and 
the next ; care being taken to exclude air bubbles. When 
a sufficient number have been assembled hot they are put 
under pressure to cool, and afterwards adjusted. Small 
condensers of similar construction are used in connexion 
with induction coils (Fig. 135). 

303. Practical Unit of Capacity. — Electricians adopt 
a unit of capacity, termed one farad, based on the system 
of electromagnetic units. A condenser of one farad 
capacity would be raised to a po- 
tential of one volt by a charge of 
one coulomb of electricity.* In 
practice such a condenser would be 
too enormous to be constructed; 
the earth itself, as an isolated 
sphere, has a capacity of only 
__i-^ of a farad. As a practical 
luiit of capacity is therefore chosen 
'^°' "*■■ the microfarad, or one millionth 

of a farad ; a capacity about equal to that of three miles 
of an Atlantic cable. Condensers of only \ microfarad 
capacity are about equal to one nautical mile of cable. 
They contain about 1200 square inches of foil. The 

* See list of Practical Electromagnetic Units, Art. 354. 




CHAP. IV CALCULATION OF CAPACITY 289 

dielectric iu them is usually mica, in thin sheets. Their 
general form is shown in Fig. 159. The two brass pieces 
upon the ebonite top are connected respectively with the 
two series of alternate sheets of tinfoil. The plug between 
them serves to keep the condenser discharged when not 
in use. 

Methods of measm'ing the capacity of a condenser 
are given iu Art. il8. 

304. Formulae for Capacities of Conductors and 
Condensers. — The following formulae give the capacity 
of condensers of all ordinary forms, iu electrostatic 
units : — 

Sphere: (radius = r. See Art. 271). 

K = r. 
Tlco Concentric Spheres: (radii r and r', dielectric 
capacity, k). 

rr' 



r' — r 
Cylinder: (length = Z, radius = r). 

2 log,'- 
r 

Two Concentric Cylinders: (length = I, dielectric 

capacity = k, internal radius = r, external radius 

K = k — L_. 

2log:- 

Circular Disk: (radius = r, thickness negligible). 

K = 2 r/TT. 
Two Circular Disks : (like air condenser. Art. 50, 
radii = r, surface = S, thickness of dielectric = b, 
dielectric capacity = k). 

K = kry4:b, 
or K = kS/4:7rb. 



290 ELECTRICITY AND MAGNETISM part ii 

The latter formula applies to any two parallel disks 
of surface S, whether circular or otherwise, provided they 
are large as compared with the distance h between them. 
To calculate down to microfarads the numbers given by 
any of the above must be divided by 900,000. 

305. Energy of Discharge of Ley den Jar or Con- 
denser. — It follows from the definition of potential, 
given in Art. 263, that in bringing up one + unit of 
electricity to the potential V, the work done is V ergs. 
This assumes, however, that the total potential Y is not 
thereby raised, and on this assumption the work * done 
in bringing up Q units would be QV ergs. If, however, 
the potential is nothing to begin with, and is raised to V 
by the charge Q, the average potential during the opera- 
tion is only ^V ; hence the total work done in bringing up 
tne charge Q from zero potential to potential V is iQV 
ergs. Now, according to the principle of the conservation 
of energy, the work done in charging a jar or condenser 
with electricity is equal to the work w^hich could be done 
by that quantity of electricity when the jar is discharged. 
Hence ^QY represents also the energy of the discharge. 

Since Q = YK, it follows that we may write iQY in 

the form J-f^. That is to say, if a condenser of capacity K 

is charged by having a charge Q imparted to it, the energy 
of the charge is proportional directly to the square of the 
quantity, and inversely to the capacity of the condenser. 

306. Symbol for Condenser. — Electricians use as 
symbols for condensers in diagrams of electric circuits 

those given in Fig. 160. 
The origin of these 



r^^ 




symbols is the alternate 
layers of tinfoils. The 
'^" ■ symbol on the right 

suggests six layers of foil, of which the first, third, and 

* If Q is piven in coulombs and V in volts, the work will be expressed 
not in ergs but \n joules (Art. 354). 



CHAP. IT CAPACITIES IX PARALLEL 291 

fifth are joined together, and the second, fourth, and 
sixth are also joined together. 

307. Capacities joined in ParalleL — To join two 
condensers together in parallel the positive foils of one 
are joined to the positive foils of the other, and their 
negative foils are also joined together. In Fig. 161 the 
two condensers K^ and Ko are joined in parallel. They 
will thus act simply like one large condenser of capacity 
= K^ 4- Kg- ^^^J charge flowing in on the + side will 
divide between the two in proportion to their capacities. 

If two equal Ley den jars are charged to the same 
potential, and then their inside and outside coatings are 
respectively joined, their 
united charge will be the 
same as that of a jar of 
equal thickness, but hav- 
ing twice the amount of 
surface. 

K a charged Leyden j,. ^^^ 

jar is placed similarly in 

communication with an uncharged jar of equal capacity, 
the charge will be shared equally between the two jars, 
and the passage of electricity from one to the other will be 
evidenced by the production of a spark when the respective 
coatings are put into communication. Here, however, half 
the energy of the charge is lost in the operation of sharing 
the charge, for each jar will have only JQ for its charge 
and JV for its potential ; hence the energy of the charge 
of each, being half the product of charge and potential, will 
only be one quarter of the original energy. The spark 
which passes in the operation of dividing the charge is, 
indeed, evidence of the loss of energy ; it is about half as 
powerful as the spark would have been if the first jar had 
been simply discharged, and it is just twice as powerful 
as the small sparks yielded finally by the discharge of 
each jar after the charge has been shared between them. 

The energy of a charge of the jar manifests itself, as 




292 ELECTRICITY AND MAGNETISM part ii 

stated above, by the production of a sj^ark at discharge ; 
the sound, light, and heat produced being the equivalent 
of the energy stored up. K discharge is effected slowly 
through a long thin w^ire of high resistance the air spark 
may be feeble, but the wire may be perceptibly heated. 
A wet string being a feeble conductor affords a slow and 
almost silent discharge ; here probably the electrolytic 
conduction of the moisture is accompanied by an action 
resembling that of secondary batteries (Lesson 492) tend- 
ing to prolong the duration of the discharge. 

308. Capacities joined in Series. — If two condensers 
are joined in series they will act as a condenser having a 
lesser capacity thau either of them separately. Their 
joint capacity in series loill be the reciprocal of the sum of the 
reciprocals of their capacities separately. 

Proof. — Let two condensers K^ and K2 be set in series (Fig. 

162) between two points across wliich there is a difference of 
potential V. This difference of 
potential will be divided between 
the two inversely in proportion 
to their capacities, seeing that 
the quantities of electricity that 
are displaced into and out of 
'fi"- 162 their respective coatings are nec- 

essarily equal. Or, if Q be this 

quantity, and K3 the effective or joint capacity of the two 

together, to find the latter, we have : — 

Q = ViKi = V,K2 - VK3 ... (1) 

and V=Vi + V.3 (2) 

From (1) we get 

Vi = VK3/K1, 
and 

V, = VK3/K2. 

Inserting these in (2) we get 

V = VK3/Ki + VK3/K2; 
whence, di\ading down by VK3, we get 

^ = ^ + ^ - , , . Q.E.D. 

K3 Ki K2 




CHAP. IV PHENOMENA OF DISCHARGE 293 



Example. — If two condensers, respectively 3 and 2 microfarads, are 
joined in series, the}- will act as a single condenser of capacity 
=^ (I + 5) = 1 5 microfarads. yV -y ft v\ P 

309. Charge of Jars arranged in Cascade. — Frank- 
lin suggested that a series of jars might be arranged, 
the outer coating of one being connected with the inner 
one of the next, the outer coating of the last being con- 
nected to earth. The object of this arrangement was that 
the second jar might be charged with the electricity 
repelled from the outer coating of the first, the third from 
that of the second, and so on. This " cascade " arrange- 
ment, however, is of no advantage, the sum of the 
charges accumulated in the series being only equal to that 
of one single jar if used alone. For if the inner coating 
of the first jar be raised to V, that of the outer coating of 
the last jar remaining at zero in contact wdth earth, the 
difference of potential between the outer and inner coat- 
ing of any one jar will be only -V, where n is number of 

n 
jars. And as the charge in each jar is equal to its 
capacity K, multiplied by its potential, the charge in 

each will only be -KV, and in the whole n jars the total 

n 

charge will be n-\v\, or KV, or eqaals the charge of one 

n 
jar of capacity K raised to the same potential V. 



Lesson XXIV. — Phenomena of Discharge 

310. Conductive Discharge. — An electrified conduc- 
tor may be dischai-ged in at least three different ways, 
depending on the medium through which the discharge 
is effected, and varying with the circumstances of the dis- 
charge. If the discharge takes place by the passage of 
a continuous current, as when electricity flows through 
a thin wire connecting the knobs of an influence machine, 
or joining the positive pole of a battery to the negative 



29i ELEClTvICITY AND MAGNETISM past ii 

pole, the operation is termed a "conductive" discharge. 
Under some circumstances a conductive discharge takes 
the nature of an oscillation to and fro (Art. 515). 

311. Disruptive Discharge. — It has been shown 
how influence across a non-conducting medium is always 
accompanied by a mechanical stress upon the medium ; 
the tension along the electi'ic lines of force increasing as 
the square of the intensity of the electric field. If this 
stress is very great the non-conducting medium will 
suddenly give way and a sparl: will burst across it. 
Such a discharge is called a " disruptive " discharge. 

A very simple experiment will set the matter in a 
clear light. Suppose a metal ball charged with -f elec- 
trification to be hung by a silk string above a metal plate 
lying on the ground. If we lower down the suspended 
ball a spark will pass between it and the plate when they 
come very near together, and the ball will then be found 
to have lost all its previous charge. It was charged with 
a certain quantity of electricity ; and as it had, when 
suspended out of the range of other conductors, a certain 
capacity (numerically equal to its radius in centimetres), 
the electricity on it would be at a certain potential 
(namely = Q/K), and the charge would be distributed 
uniformly all over it. The plate lying on the earth 
would be all the while at zero x^otential. But when the 
suspended ball was lowered down towards the plate the 
previous state of things was altered. In the i)resence of 
the + charge of the ball the potential* of the plate 
would rise, were it not that, by influence, just enough 
negative electrification appears on it to keep its potential 
still the same as that of the earth. The tension in the 
electric field will draw the -f charge of the ball down- 
wards, and alter the distribution of the charge, the surface- 
density becoming greater at the under surface of the ball 

* The student must remember that, by the definition of potential in 
Art. 263, the potential at a point is the simi of all the separate quantities of 
electricity near it, di\-ided each by its distance from the point. 



CHAP. IV LENGTH OP SPAEIv 295 

and less on the upper. The capacity of the ball will be 
increased, and therefore its potential will fall corre- 
spondingly. The layer of air between the ball and the 
plate is acting like the glass of a Ley den jar. The more 
the ball is lowered down the greater is the accumulation 
of the opposite kinds of charge on each side of the layer 
of air, and the tension across the layer becomes greater 
and greater, until the limit of the dielectric strength is 
reached; the ak suddenly gives way and the spark tears 
a path across. 

312. Convective Discharge. — A third kind of dis- 
charge, differing from either of those above mentioned, 
may take place, and occurs chiefly when electricity of a 
high potential discharges itself at a pointed conductor by 
accumulating there with so great a density as to electrify 
the neighbom-ing particles of air ; these particles then 
flying off by repulsion, conveying away part of the charge 
with them. Such convective discharges may occur either 
in gases or in liquids, but are best manifested in air and 
other gases at a low pressure, in tubes exhausted by an 
air pump. 

The discharge of a quantity of electricity in any of the 
above ways is always accompanied by a transformation of 
its energy into energy of some other kind, — sound, light, 
heat, chemical actions, and other phenomena being pro- 
duced. These effects must be treated in detail. 

313. Length of Spark. — Generally speaking, the 
length of spark between two conductors increases with 
the difference between then- potentials. It is also found 
to increase w^hen the pressure of the air is diminished. 
Riess found the distance to increase in a proportion a 
little exceeding that of the difference of potentials. Lord 
Kelvin confirmed this by measuring by means of an 
"absolute electrometer" (Art. 287) the difference of 
potential necessary to produce a spark discharge between 
two parallel plates at different distances. De la Rue 
and Miiller found with their great battery (Art. 186) 



296 ELECTRICITY AND MAGXETISM part ii 

that with a difference of j)otential of 1000 volts the strik- 
ing distance of the spark was only -0127 centimetres (or 
abont 2^ of an inch), and with a difference of 10,000 
Tolts only 1-369. Theii' 11,000 sHver ceUs gave a spark 
of 1-59 centim. (about f of an inch) long. To produce a 
spark one mile long, through air at the ordinary pressure, 
would therefore require a difference of potential exceed- 
ing that furnished by 1,000,000,000 DanieU's cells ! 

The length of the spark differs in different gases, 
being nearly twice as long in hydrogen as in air at the 
same density. Or to produce in hydrogen a spark as 
long as one in air requires less voltage. On the other 
hand, carbonic acid gas, whUst it is stronger than air for 
short sparks, is weaker for long ones. 

The j)otential needful to produce a spark of given 
length in a given gas is independent of the kind of metal 
used as electrodes, but de]Dends upon theu' shape. If 
IDoints are used tustead of balls it is found that at equal 
voltage, points are best for long sparks, but are worst for 
short sparks. 

According to Peace's observations a minimum poten- 
tial of between 300 and 100 volts is necessary to start a 
spark, however short, in air. For sparks not under two 
millimetres in length the volts necessary to start a spark 
across a length of I centimetres may be approximately 
expressed by the equation — 

Y= 1500 -r 30,000 L 

The followiug table, calculated from the results of 
Heydweiller, gives the volts necessaiw to produce a spark 
in air at 15^ C. and 76 centimetres pressure between two 
spheres of various sizes. The figures must be increased 1 
per cent for a fall of 3 degrees of temperatiu'e, or for a 
rise of 8 millimetres of pressure. 



CHAP. IT 



LENGTH OF SPARK 



297 



Eadius of Balls. 


Distance between Balls (Centims.). 


0-1 


0-5 


1-0 


1-5 


Centims. 
2-5 


Volts. 
4500 


Volts. 
18900 


Volts. 
33840 


Volts. 
47610 


1-0 


4860 


18030 


32120 


41160 


0-5 


4950 


17790 


27810 


32400 


0-25 


1 
4980 1 1G200 

i 


20790 


22980 



In rarefied air the spark is longer. Snow Harris 
stated that the length of spark was inversely propor- 
tional to the pressui'e, but this law is not quite correct, 
being approximately true only for pressures between 
that of 11 inches of mercury and that of 30 inches (one 
atmosphere). At lower pressures, as Gordon found, a 
greater difference of potential must be used to produce 
a spark than that which would accord with Harris's law. 
From this it would apj)ear that thin layers of air oppose 
a proportionally greater resistance to the piercing power 
of the spark than thick layers, and possess greater dielec- 
tric strength. 

Faraday, using two spheres of different sizes, found 
the spark-length greater when the smaller sphere was 
positive than when it was negative. 

With rapidly alternating differences of potential, 
smaller virtual voltages suffice for the same spark-length, 
for the length depends on the maximum, not on the 
mean value. Using a ball of 1 cm. diameter and a disk, 
Alexander Siemens found 3200 virtual volts to be needed 
at 0-1 cm. distance, and 11,000 at 0-5 cm. distance apart. 

The dielectric strength of a gas appears to be weaker 
when field is vai-ying than when it is steady. ^Vhell the 



298 ELECTRICITY AND MAGNETISM part li 

voltage is nearly high enough to produce a spark, revers- 
ing the poles will sometimes start a spark. Moreover, 
when once a spark has iDassed it is easier for a second one 
to follow on the same track. Probably the first spark 
produces chemical dissociations in its path which do not 
instantly pass away. 

Hertz made the singular observation that ultra-violet 
light (i.e. actinic waves) falling upon the kathode surface 
assist it to discharge (see Art. 351). 

A perfect vacuum is a perfect insulator — no spark 
will cross it. It is j)ossible to exhaust a tube so perfectly 
that none of our electric machines or appliances can send 
a spark through the vacuous space even over so short a 
distance as one centimetre. 

On the other hand, a great increase of pressure also 
increases the dielectric strength of air, and causes it to 
resist the passage of a spark. Cailletet compressed dry 
air at 40 to 50 atmospheres' i3ressure, and found that 
even the spark of a powerful induction coil failed to 
cross a space of -05 centimetres' width. 

314. Flames and Hot Air. — The arc produced by 
the passage of an electric current between two carbon 
poles is treated of in Art. 448. It is a species of flame 
which conducts the current from the tip of one carbon 
rod to the other, while volatilizing the carbon, and requires 
only some thkty to fifty volts for its maintenance. The 
alternate-current arc generated in air by high-frequency 
discharges at a iDotential of 10,000 to 50,000 volts is a 
different phenomenon, and is apparently an endothermic 
flame of nitrogen and oxygen bm'ned together. 

Sparks are longer and straighter through hot air 
than through cold. K air or other permanent gas is, 
however, heated in a closed vessel so that its density 
remains unaltered, the voltage needful to produce dis- 
charge remains the same ; unless, indeed, the gas be 
heated to point of dissociation Avhen discharge occurs at 
low voltao'e. 



CHAP. IV PROPERTIES OF ELAME 299 

Flames and cnrrents of ver}^ hot air, such as those 
rising from a red-hot piece of ii'on, are extremely good 
conductors of electricity, and act even better than 
metallic points in discharging a charged conductor. 
Gilbert showed that an electrified body placed near a 
flame lost its charge ; and the very readiest way to rid 
the surface of a charged body of low conducting power of 
a charge imparted to it by friction or otherwise, is to pass 
it through the flame of a spirit-lamp. Faraday found 
negative electrification to be thus more easily discharged 
than positive. Flames powerfully negatively electrified 
are repelled from conductors, though not so when posi- 
tively electrified. Sir W. Grove showed that a current 
is set up in a platinum wire, one end of which touches 
the tip, and the other the base, of a flame. 

Guthrie showed that a red-hot iron ball cannot be 
positively, but may be negatively charged. When white- 
hot it will retain neither kind of charge. 

315. Mechanical Effects. — Chief amongst the me- 
chanical effects of the disruptive spark discharge is the 
shattering and piercing of glass and other insulators. 
The dielectric strength of glass, though much greater 
than that of air, is not infinitely great. A slab of glass 
3 inches thick has been pierced by the discharge of a 
powerful induction coil. The so-called " toughened " 
glass has a greater dielectric strength than ordinary glass, 
and is more difficult to pierce. A sheet of glass may be 
readily pierced by a spark from a large Leyden jar or 
battery of jars, by taking the following precautions: — 
The glass to be x^ierced is laid upon a block of glass or 
resin, through which a wire is led by a suitable hole, one 
end of the wire being connected with the outer coating 
of the jar, the other being cut off flush with the surface. 
Upon the upper surface of the sheet of glass that is to be 
pierced another wire is fixed upright, its end being exactly 
opposite the lower wire, the other extremity of this wire 
being armed with a metal knob to receive the spark from 



300 ELECTRICITY AND MAGNETISM part ii 

the knob of the jar or discharger. To ensure good insula- 
tion a few drops of paraffin oil, or of olive oil, are placed 
upon the glass round the points where the wires touch it. 
A piece of dry wood similarly treated is split by a power- 
ful spark. A layer of oil resists being pierced as much 
as a layer of air five or six times as thick would do. 

If a spark is led through a tightly-corked glass tube 
containing w^ater, the tube will be shattered into small 
pointed fragments by the sudden expansion of the liquid. 

Lullin observed two curious effects when a x)iece of 
cardboard is perforated by a spark between two metal 
points. Firstly, there is a slight burr raised on each side, 
as if the hole had been pierced from the middle outwards, 
as though the stress in the air had pulled at the card. 
Secondly, if the two points are not exactly opposite one 
another the hole is found to be nearer the negative point. 
But if the experiment is tried under the air pump in a 
vacuum, there is no such displacement of the hole ; it is 
then midway exactly. 

The mechanical action of the brush discharge at 
points is mentioned in Art. 47, and the mechanical 
effects of a current of electricity were described in 
Lesson XYI. 

316. Chemical Effects. — The chemical actions pro- 
duced by currents of electricity have been described in 
Lessons XIY. and XIX. Similar actions can be produced 
by the electric spark, and by the silent glow discharge 
(see Art. 319). Faraday showed, indeed, that electricity 
from all kinds of different sources produced the same 
kinds of chemical actions, and he relied upon this as one 
proof of the essential identity of the electricity produced 
in different ways. If sparks from an electric machine are 
received upon a piece of white blotting-paper moistened 
with a solution of iodide of potassium, brown patches are 
noticed where the spark has effected a chemical decom- 
position and liberated the iodine. 

When a stream of sparks is passed through moist au- 



CHAP. IV CHEMICAL ACTION OF SPARKS 301 

in a vessel, the air is found to have acquired the property 
of changing to a red colour a piece of paper stained blue 
with litmus. This, Cavendish showed, was due to the 
presence of nitric acid, produced by the chemical union 
of the nitrogen and oxygen of the air. The effect is best 
shown with the stream of sparks yielded by a small in- 
duction coil (Fig. 135), in a vessel in which the air has 
been compressed beyond the usual atmospheric pressure. 

Whenever an electric machine is giving out high-volt- 
age discharges a peculiar odour is perceived. This was 
formerly thought to be evidence of the existence of an 
electric " effluvium " or fluid ; it is now known to be 
due to the presence of ozone, a modified form of oxygen 
gas, which differs from oxygen in being denser, more 
active chemically, and in having a characteristic smell. 
The silent discharge of the influence machine and that of 
the induction coil are particularly favourable to the pro- 
duction of this substance. 

The spark will decompose ammonia gas, and olefiant 
gas, and it will also cause chemical combination to take 
place with explosion, when passed through detonating- 
mixtures of gases. Thus equal volumes of chlorine and 
hydrogen are exploded by the spark. So are oxygen and 
hydrogen gases, when mixed in the proportion of two 
volumes of the latter to one of the former. Even the 
explosive mixture of common coal gas mixed with from 
four to ten times its own volume of common air, can be 
thus detonated. A common experiment with the so-called 
electric j)istol consists in filling a small brass vessel with 
detonating gases and then exploding them by a spark. 
The spark discharge is sometimes applied to the firing of 
blasts and mines in military operations. 

317. Heating Effects. — The flow of electricity 
through a resisting medium is in every case accompanied 
by an evolution of heat. The laws of heating due to 
currents are given in Art. 427. The disruptive discharge 
is a transfer of electricity through a medium of great re- 



302 ELECTRICITY AXD MAGNETISM paet ii 

sistance and accompanied by an evolution of heat, A few 
drops of ether in a metallic spoon are easily kindled by 
an electric spark. The spark from an electric machine, 
or even from a rubbed glass rod, suffices to kindle an 
ordinary gas-jet. In certain districts of America, during 
the driest season of the year, the mere rubbing of a per- 
son's shoes against the carpet, as he shuffles across the 
floor, generates sufficient electrification to enable sparks 
to be drawn from his body, and he may light the gas by 
a single spark from his outstretched finger. Gunpowder 
can be fired b}' the discharge of a Leyden jar, but the 
spark should be retarded by being passed through a wet 
thread, otherwise the powder will simply be scattered by 
the spark. 

The Electric Air-Thermometer, invented by Kinnersley,* 
serves to investigate the heating powers of the discharge. 
It consists of a glass vessel enclosing air, and communi- 
cating with a tube partly filled with water or other liquid 
in order to observe changes of volume or of pressure. 
Into this vessel are led two metal rods, between which is 
suspended a thin wire, or a filament of gilt paper ; or a 
spark can be allowed simply to cross between them. 
When the discharge passes the enclosed air is heated, 
expands, and causes a movement of the indicating column 
of liquid. The results of observation with these instru- 
ments are as follows : — The heating effect produced by a 
given charge in a wire of given length is inversely 
proportional to the square of the area of the cross section 
of the wire. The total heat evolved is jointly propor- 
tional to the charge, and to the potential through which 
it falls. In fact, if the entire energy of the discharge is 
expended in producing heat, and in doing no other kind 
of work, then the heat developed will be the thermal 

* This instrument diflFers in no essential respect from that devised 
ninety years later hy Eiess, to whom the instrument is often accredited. 
Eiess, however, deduced quantitative laws, while Kinnerslej' contented 
himself with qualitative observations. 



CHAP. IV LUMINOUS DISCHARGES 303 

QY 

eiiuivalent of IQY ergs, or — calories; where J re- 
presents the mechanical equivalent of heat (J = 42 
million; since 42 x 10^ ergs = 1 calorie), and Q and V 
are expressed in C.G.S. units. 

"\A"hen a powerful discharge takes place through very- 
thin wires, they may be heated to redness, and even fused 
by the heat evolved. Van Marum thus once heated 70 
feet of wire by a powerful discharge. A narrow strip of 
tinfoil is readily fused by the charge of a large Ley den 
jar, or battery of jars. A piece of gold leaf is in like 
manner volatilized by a powerful discharge. Franklin 
utilized this property for a rude process of multiplying 
portraits or other patterns, which, being first cut out in 
card, were reproduced in a silhouette of metallic particles 
on a second card, by the device of laying above them a 
film of gold or silver leaf covered again with a piece of 
card or paper ; a Leyden battery being then discharged 
through the leaf. 

318. Luminous Effects. — The discharge exhibits 
many beautiful and varied luminous effects under dif- 
ferent conditions. The spark of the disruptive discharge 
is usually a thin brilliant streak of light. When it takes 
place between two metallic balls, separated only by a 
short interval, it usually appears as a single thin and 
brilliant line. If, however, the distance be as much as a 
few centimetres, the spark takes an irregular zig-zag form. 
In any case its path is along the line of least resistance, 
the presence of minute motes of dust floating in the air 
being quite sufficient to determine the zig-zag character. 
Often the spark exhibits curious ramifications and fork- 
ings, of which an illustration is given in Fig. 163, which 
is drawn of one-eighth of the actual size of the spark 
obtained from an electrical machine. Photographs of 
lightning flashes almost always show similar branching. 
The branches always point toward the negative electrode. 
The discharge from a Leyden jar affords a much brighter, 



304 ELECTRICITY AND MAGNETISM part ii 

shorter, noisier spark than the spark drawn direct from 
the collector of a machine. The length (see Art. 313) 
depends upon the potential, and upon the pressure and 
temperature of the air in which the discharge takes place. 
The brilliance depends chiefly upon the quantity of the 
discharge. The colour of the spark varies with the na- 
ture of the metal surfaces between which the discharge 




Fig. 163. 

takes place ; for the spark tears away in its passage small 
portions of the metal surfaces, and volatilizes them. 
Between copper or silver terminals the spark takes a 
green tint, w^hile between iron knobs it is of a reddish 
hue. Examination with the spectroscope reveals the 
presence in the spark of the rays characteristic of the 
incandescent vapours of the several metals. 

319. Brush Discharge: Glow Discharge. — If an elec- 
tric machine is vigorously worked, but no sparks be 
drawn from its collector, a fine diverging brush of pale 
blue light can be seen (in a dark room) streaming from 
the brass ball at the end of it farthest from the col- 
lecting comb ; a hissing or crackling sound always accom- 
panies this kind of discharge. The brush discharge 
consists of innumerable fine twig-like ramifications, pre- 
senting a form of which Fig. 164 gives a fine example. 
The brightness and size of the hrmJi is increased by 
holding a flat plate of metal a little way from it. With 



CHAP. IV BEUSH AND GLOW 305 

a smaller ball, or with a bluntly-pointed wire, the brush 
appears smaller, but is more distinct and continuous. 
^Vhen discharge is going on between two balls the 
brushes are never alike. At the positive ball or anode 
the brush discharge is larger and more ramified than at 
the negative ball. But the negative brush is more easily 
formed than the positive. Wheatstone found by using his 
rotating mirror that the brush discharge is really a series 




Fig. 164. 

of successive partial sparks at rapid intervals. Metallic 
dust is in every case torn away from the electrode by the 
brush discharge. 

If the blunt or rounded conductor be replaced by a 
pointed one, the brush disappears and gives place to a 
quiet and continuous glow where the electrified particles 
of air are streaming away at the point. If these con- 
vexion streams are impeded the glow may once more 
give place to the brush. Where a negative charge is 
being discharged at a point, the glow often appears to 
be separated from the surface of the conductor by a dark 
space, where the air, without becoming luminous, still 



306 ELECTRICITY AND MAGNETISM part ii 

conveys the electricity. This phenomenon, to which 
Faraday gave the name of the '■'- dark" discharge, is very 
well seen when electricity is discharged tlirough rarefied- 
air and other gases in vacuum tubes. 

A spark discharge may degenerate into a brush if the 
surface of the electrode becomes pitted or roughened by 
frequent discharges. Hence in all spark experiments it is 
important to keep the discharging balls highly polished. 

320. Discharges in Partial Vacua. — If the discharge 
takes place in glass tabes or vessels from which the air 
has been partially exhausted, many remarkable and beau- 
tiful luminous phenomena are produced. A common 
form of vessel is the " electric egg " (Fig. 137), a sort of 
oval bottle that can be screwed to an air pump, and 




Fig. 165. 

furnished with brass knobs to lead in the sparks. More 
often "vacuum tubes," such as those manufactured by 
the celebrated Geissler, are employed. These are merely 
tubes of thin glass blown into bulbous or spiral forms, 
provided with two electrodes of platinum wire fused into 
the glass, and sealed off after being partially exhausted 
of air by a mercurial air pump. Of these Geissler tubes 
the most useful consist of two bulbs joined by a narrow 
tube (Fig. 165), the luminous effects being usually more 
intense in the contracted portion. Such tubes are readily 
illuminated by discharges from an electrophorus or an 



CHAP. IV VACUUM TUBES 307 

influence machine ; but it is more common to work them 
with the spark of an induction coil (Fig. 135). A coil 
capable of throwing a ^-iiich spark in air will illuminate 
a vacuum tube 6 or 8 inches long. Where an alternate- 
current supply is available small transformers (Art. 228) 
wound to deliver ^^ ampere at 5000 volts serve admirably 
for lighting vacuum tubes. 

Through such tubes, before exhaustion, the spark 
passes without any unusual phenomena being produced. 
As the air is exhausted the sparks become less sharply 
defined, and widen out to occupy the whole tube, becom- 
ing pale in tint and nebulous in form. The kathode 
exhibits a beautiful bluish or violet glow, separated from 
the conductor by a narrow dark space, while at the anode 
a single small bright star of light is all that remains. 
At a certain degTee of exhaustion the light in the tube 
breaks up into a set of strice, or patches of light of a cup- 
like form, which vibrate to and fro between darker spaces. 
In nitrogen gas the violet aureole glowing around the 
kathode is very bright, the rest of the light being rosy 
in tint. In oxygen the difference is not so marked. In 
hydrogen gas the tint of the discliarge is bluish, except 
where the tube is narrow, where a beautiful crimson may 
be seen. With carbonic acid gas the light is remarkably 
white. Particles of metal are torn off from the kathode, 
and projected from its surface. The kathode is also usu- 
ally the hotter when made of similar dimensions to the 
anode. If the anode is heated and the kathode kept 
cool no discharge will pass. The luminosity disappears 
from the rarefied air in the neighbourhood of a red-hot 
platinum spiral inside the tube. If the kathode gets 
white-hot the glow disappears, and the gas conducts 
freely without shining. It is also observed that the light 
of these discharges in vacuo is rich in those rays which 
produce phosphorescence and fluorescence. Many beau- 
tiful effects are therefore produced by blowing tubes in 
uranium glass, which fluoresces with a fine green light, 



308 ELECTRICITY AND MAGNETISM pakt ii 

and by placing solutions of quinine or other fluorescent 
liquids in outer tubes of glass. 

321. Phenomena in High Vacua. — Crookes has found 
that when exhaustion is carried to a very high degree the 
dark space separating the negative glow from the negative 
pole increases in width; and that across this space elec- 
trified molecules are projected in parallel paths normally 
from the surface of the kathode. If exhaustion be carried 
to such a high degree that the dark space fills the entire 
tube or bulb, the glass walls become beautifully phos- 
phorescent. Diamonds, rubies, and even white powdered 

alumina placed in the 
tubes become brill- 
iantly phosphorescent 
if the kathode dis- 
charge is directed upon 
them. And if bodies 
(whether opaque or 
transparent) be inter- 
posed in front of the 
electrode, sharply-de- 
Pig 166. fined shadows of these 

bodies are projected 
upon the opposite wall of the vessel, as if they stopped 
the way for some of the flying molecules, and prevented 
them from striking the opposite wall. In Fig. 166 the 
kathode K is a slightly convex disk of aluminium. In 
the path of the discharge is set a cross cut out of mica. 
Its shadow S appears on the end of the bulb, which phos- 
phoresces all around the shadowed part. The anode may 
be either at A or a. Lightly-poised vanes are also driven 
round if placed in the path of the discharge. Crookes 
regarded this kathode discharge as exhibiting matter in 
an ultra-gaseous or radiant state. A disk placed in the 
line of the kathode discharge becomes thereby posi- 
tively electrified. The kathode discharge is independent 
of the metal used as kathode, and is also independent of 




CHAP. IT EFFECTS IN HIGH VACUA 309 

the position of the anode. Any restriction of space 
around the kathode tends to stop the discharge. Similar 
phenomena have been observed in vacuous tubes without 
any internal electrodes. Hertz discovered that these 
kathodic " rays " which will not pass through glass, mica, 
or any transparent substance, will pass through metal 
foil. Lenard, using a vacuum tube with a " window " of 
aluminium foil at one end, has succeeded in passing the 
kathodic rays out into the air (in which they cannot 
be produced at all), and finds them to retain their re- 
markable property of exciting phosphorescence. 

In extremely high vacua there is an enormous re- 
sistance, apparently due to some difficulty in the electric 
discharge leaving the electrode. The molecular con- 
ductivity of the rarefied gas is itseK very high. For 
an equal number of molecules it is higher than that of 
the metals. 

Holtz has more recently produced " electric shadows," 
by means of discharges in air at ordinary pressure, be- 
tween the poles of the influence machine (Fig. 41), the 
discharge taking place between a point and a disk covered 
with silk, on Avhich the shadows are thrown. 

322. Striae. — The strice or stratijications have been 
exammed very carefully by Gassiot, by Spottiswoode, and 
by De la Rue. The principal facts hitherto gleaned are 
as follow : — The striae originate at the anode at a certain 
pressure, and become more numerous, as the exhaustion 
proceeds, up to a certain point, when they become thicker 
and diminish in number, until exhaustion is carried to 
such a point that no discharge will pass. J. J. Thomson 
found the column of striae to exhibit a nearly constant 
electric resistance all along; though beyond it in the 
neighbourhood of the kathode the resistance was much 
greater. In a vacuum tube over 50 feet long the dis- 
charge was striated through whole length except near the 
kathode. If the kathode is moved forward the striae 
move with it. The striae flicker even when the con- 



310 ELECTRICITY AND MAGNETISM part ii 

tiimous current from a battery of some thousands of cells 
(Art. 186) is used. There is a maximum of steadiness 
with a particular density of cm^rent. The strise are hotter 
than the spaces between them. The number and position 
of the strise vary, not onl}^ with the exhaustion, but with 
the difference of potentials of the electrodes. Each portion 
of the column of strise acts as an independent discharge. 
When striae are produced by the intermittent discharges 
of the induction coil, examination of them in a rotating 
mirror reveals that they move forward from the anode 
towards the kathode. 

Schuster has shown that the discharge through gases 
is a process resembling that of electrolysis (Art. 237), 
being accompanied bj^ breaking up of the gaseous mole- 
cules and incessant interchanges of atoms between them. 
The production of ozone (Art. 316) and the phenomena 
noticed at the kathode (Art. 321) give support to this 
view. Amongst other evidence is the striking discovery 
of Hittorf that quite a few cells can send a current 
through gas at ordinary pressures provided a spark-dis- 
charge is going on in the neighbourhood. J. J. Thomson 
finds that those gases which when heated are decomposed 
or molecularly dissociated, so that free atoms are present, 
are also good conductors. He regards chemical decom- 
position as an essential feature of gaseous discharge. 

The discharges in vacuum tubes are affected by the 
magnet at all degrees of exhaustion, behaving like flexible 
conductors. Under certain conditions also, the discharge 
is sensitive to the presence of a conductor on the exterior 
of the tube, retreating from the side where it is touched. 
This sensitive state appears to be due to a periodic inter- 
mittence in the discharge ; an intermittence or partial 
intermittence in the flow would also probably account for 
the production of striae. 

323. Velocity of Propagation of Discharge. — The 
earliest use of the rotating mirror to analyze pheno- 
mena of short duration was made by "Wheatstone, who 



CHAP. IV VELOCITY OF PROPAGATION 311 

attempted by this means to measure " the velocity of 
electricity" in conducting wkes. What he succeeded in 
measming was not, however, the velocity of electricity, but 
the time taken by a certain quantity of electricity to 
flow through a conductor of considerable resistance and 
capacity. Viewed in a rotating mirror, a spark of definite 
duration would appear to be drawn out into an elongated 
streak. Such an elongation was found to be visible when 
a Ley den Jar was discharged through a copper wire half 
a mile long; and when the cu'cuit was interrupted at 
three points, one in the middle and one at each end of this 
wu'e, three sparks were obtained, which, viewed in the 
mirror, showed a lateral displacement, indicating (with 
the particular rate of rotation employed) that the middle 
spark took place jtsto oo of ^ second later than those at the 
ends. Wheatstone argued from this a velocity of 288,000 
miles per second. But Faraday showed that the apparent 
rate of propagation of a quantity of electricity must be 
affected by the capacity of the conductor ; and he even 
predicted that since a submerged insulated cable acts like 
a Leyden jar (see Art. 301), and has to be charged before 
the potential at the distant end can rise, it will retard 
the ajDparent flow of electricity through it. Professor 
Fleeming Jenkin says of one of the Atlantic cables that, 
after contact with the battery is made at one end, no 
effect can be detected at the other for two-tenths of a 
second, and that then the received current gradually 
increases, until about three seconds afterwards it reaches 
its maximum, and then dies away. This retardation is 
proportional to the square of the length of the cable, being 
proportional both to its capacity and to its resistance ; 
hence it becomes very serious on long cables, reducing the 
speed of signalling. There is in fact no definite assign- 
able "velocity of electricity." In the case of wires 
suspended in air the velocity of propagation of any rapid 
electrical vibration is equal to the velocity of light. But 
in the case of slow vibrations, like those of telephonic 



312 ELECTRICITY AND MAGNETISM part ii 

sounds being sent through land lines or cables, the velo- 
city may be much less. 

A very simple experiment will enable the student to 
realize the excessively short duration of the spark of a 
Leyden jar. Let a round disk of cardboard painted 
with black and white sectors be rotated very rapidly so 
as to look by ordinary light like a mere gray surface. 
When this is illuminated by the spark of a Leyden jar it 
appears to be standing absolutely still, however rapidly 
it may be turning. A flash of lightning is equally in- 
stantaneous; it is utterly impossible to determine at 
which end the flash begins.* 

324. Electric Dust-Figures. — Electricity may creep 
slowly over the surface of bad conductors. Lichtenberg 




Tig. 167. 

devised an ingenious and easy way of investigating the 

* Sometimes the flash seems to strike downTvards from the clouds, some- 
times upwards from the earth. This is an optical illusion, resulting 
from the unequal sensitiveness to light of different portions of the retina of 
the eye. 



ELECTRIC DUST-FIGURES 



313 



distribution of electricity by means of certain electro- 
scopic powders. Take a charged Leyden jar an.d write 
with the knob of it upon a cake of pitch or a dry sheet of 
glass. Then sift, through a bit of muslin, over the cake 
a mixture of powdered red lead and sulphur (vermilion 
and lycopodiura powder answer equally well). The 
powders in this process rub against one another, the red 
lead becoming +, the sulphur — . Hence the sulphur will 




Fig. 168. 

be attracted to those parts where there is + electrification 
on the disk, and settles down in curious branching yellow 
streaks like those shown in Fig. 167. The red lead settles 
down in little red heaps and patches where the electrifica- 
tion is negative. These rounded red patches indicate that 
the — discharge has been of the nature of a in'nd or silent 
discharge. The branching yellow streaks indicate that, 
the positive discharge (as indeed may be heard) is of the 
nature of a hrush. Fig. 168 shows the general appearance 
of the Lichtenberg's figure produced by holding the knob 



314 ELECTRICITY AND MAGNETISM part ii 

of the Leyden jar at the centre of a shellac plate that has 
previously been rubbed with flannel, the negative elec- 
trification being attracted upon all sides toward the 
central positive charge. These same powders may be used 
to investigate how surfaces have become electrified by 
rubbing, and how pyroelectric crystals (Art. 74) are elec- 
trified during cooling. 

Powdered tourmaline, warmed and then sifted over a 
sheet of glass previously electrified irregularly, wall show 
similar figures, though not so well defined. 

Breath-Jigures can be made by electrifying a coin or 
other piece of metal laid upon a sheet of dry glass, and 
then breathing upon the glass where the coin lay, reveal- 
ing a faint image of it on the surface of the glass. 

F. J. Smith finds that if a coin or engraving laid face- 
down upon a photographic dry-plate is sparked with an 
induction coil, the plate receives an invisible image which 
can be photographically developed. 

325. Physiological Effects. — The physiological effects 
of the current have been described in Lesson XX. Those 
produced by the spark-discharge are more sudden in 
character, but of the same general nature. Death is 
seldom the direct result. The shock causes a sudden 
cessation of respiration, resulting in suffocation as from 
drowning. The bodies of persons struck by the lightning 
spark frequently exhibit markings of a reddish tint where 
the discharge in passing through the tissues has lacerated 
or destroyed them. Sometimes these markings present 
a singular ramified appearance, as though the discharge 
had spread in streams over the surface at its entry. 

326. Dissipation of Charge. — However well insu- 
lated a charged conductor may be, and however dry the 
surrounding air, it nevertheless slowly loses its charge, 

► and in a few days will be found to be completely discharged. 
The rate of loss of charge is, however, not uniform. It 
is approximately proportional to the difference of potential 
between the body and the earth. Hence the rate of loss 



CHAP. IV LAW OF LEAKAGE 315 

is greater at first than afterwards, and is greater for 
highly-charged bodies than for those feebly charged. The 
law of dissipation of charge therefore resembles ISTewton's 
law of cooling, according to which the rate of cooling of a 
hot body is proportional to the difference of temperature 
between it and the surrounding objects. If the potential 
of the body be measured at equal intervals of time it will 
be found to have diminished in a decreasing geometric 
series; or the logarithms of the potentials at equal in- 
tervals of time will differ by equal amounts. The rate 
of loss is, however, greater at negatively-electrified sur- 
faces than at positive. 

This may be represented by the following equation : — 

where Yo represents the original potential and Yt the potential 
after an interval t. Here e stands for the number 2-71828 . . . 
(the base of the natural logarithms), and p stands for the 
" coefficient of leakage," which depends upon tlie temperature, 
pressure, and humidity of the air. The same formula serves for 
the discharge of a condenser of capacity K through a resistance 
K ; if p is written for 1/KR. 

327. Positive and Negative Electrification. — The 

student will not have failed to notice throughout this 
lesson frequent differences between the behaviour of 
j)ositive and negative electrification. The striking dis- 
similarity in the Lichtenberg's figures, the displacement 
of the perforation-point in Lullin's experiment, the im- 
equal tendency to dissipation at surfaces, the unequal 
action of heat on positive and negative charges, the re- 
markable differences in the various forms of brush and 
glow discharge, are all points that claim attention. Gas- 
siot described the appearance in vacuum tubes as of a 
force emanating from the negative pole. Crookes's experi- 
ments in high vacua show molecules to be violently 
discharged from the negative electrode, the vanes of a 
little fly enclosed in such tubes being moved from the 
side struck by the negative discharge. Holtz found that 



316 ELECTRICITY AXD MAGNETISM part ii 

when funnel-like partitions were fixed in a vacuum tube 
the resistance is much less when the open mouths of the 
funnels face the negative electrode. These matters are 
yet quite unaccounted for by any existing theory of 
electricity. 

The author of these lessons is disposed to take the following 
view on this point: — If electricity be really one and not two, 
either the so-called positive or the negative electrification must 
be a state in which there is more electricity than in the sur- 
rounding space, and the other must be a state in which there is 
less. The student was told, in Art. 7, that in the present state 
of the science we do not know for certain whether " positive" 
electrification is really an escQss of electricity or a defect. Now 
some of the phenomena alluded to in this Article seem to in- 
dicate that the so-called '• negative" electrification really is the 
state of excess. In particular, the fact that the rate of dissipation 
of charge is greater for negative electrification than for positive, 
points this way : because the law of loss of charge is the exact 
counterpart of the law of the loss of heat, in which it is quite cer- 
tain that, for equal differences of temperature between a body 
and its surroundings, the rate of loss of heat is greater at higher 
temperatures than at lower : or the body that is really hotter 
loses its heat fastest. 



Lessox XXV. — Atmospheric Electricity 

328. The phenomena of atmospheric electricity are 
of two kinds. There are the well-known electrical pheno- 
mena of thunderstorms ; and there are the phenomena 
of continual slight electrification in the air, best observed 
when the weather is fine. The phenomena of the Aurora 
constitute a third branch of the subject. 

329. The Thunderstorm an Electrical Phenomenon. 
— The detonating sparks drawn from electrical machines 
and fi'om Leyden jars did not fail to suggest to the 
early experimenters, Hauksbee, Xewton, Wall, Xollet, 
and Gray, that the lightning flash and the thunder- 
clap were due to electric discharges. In 1749, Benja- 
min Franklin, observing lightning to possess almost aU 



CHAP. IV THUNDERSTORMS 317 

the properties observable in electric sparks,* suggested 
that the electric action of points (Art. 46), which was 
discovered by him, might be tried on thunderclouds, and 
so draw from them a charge of electricity. He proposed, 
therefore, to fix a pointed iron rod to a high tower. 
Before Franklin could carry his proposal into effect, 
Dalibard, at Marl3'-la-ville, near Paris, taking up the 
hint, erected an iron rod 40 feet high, by which, in 1752, 
he drew sparks from a passing cloud. Franklin shortly 
after succeeded in another way. He sent up a kite during 
the passing of a storm, and found the wetted string to 
conduct electricity to the earth, and to yield abundance 
of sparks. These he drew from a key tied to the string, 
a silk ribbon being interposed between his hand and the 
key for safety. Leyden jars could be charged, and all 
other electrical effects produced, by the sparks furnished 
from the clouds. The proof of the identity was complete. 
The kite experiment was repeated by Romas, who drew 
from a metallic string sparks 9 feet long, and by Cavallo, 
who made many important observations on atmospheric 
electricity. In 1753 Richmann, of St. Petersburg, who 
was experimenting with an apparatus resembling that 
of Dalibard, was struck by a sudden discharge and 
killed. 

330. Theory of Thunderstorms. — Solids and liquids 
cannot be charged throughout their substance ; if charged 
at all the electrification is upon their surface (see Art. 
41). But gases and vapours, being composed of myriads 

* Franklin enumerates specifically an agreement between electricity and 
lightning in the following respects : — Giving light ; colour of the light ; 
crooked direction ; swift motion ; being conducted by metals ; noise in 
exploding ; conductivity in water and ice ; rending imperfect conductors ; 
destroying animals ; melting metals ; firing inflammable substances ; sul- 
phureous smell (due to ozone, as we now know) ; and he had previously 
found that needles could be magnetized both by lightning and by the 
electric spark. He also drew attention to the similarity between the pale- 
blue flame seen during thundery weather playing at the tips of the masts 
of ships (called by sailors St. Elmo's Fire), and the " glow " discharge at 
points. 



318 ELECTEICITY AND MAGXETISM part ii 

of separate particles, can receive a bodily charge- The 
air in a room in which an electric machine is worked 
is found afterwards to be charged. The clouds are 
usually charged more or less with electricity, derived, 
probably, from evaporation going on at the earth's surface. 
The minute particles of water floating in the air become 
more highly charged. As they fall by gravitation and 
unite together, the strength of their charges increases. 
Suppose eight small drops to join into one. That one 
will have eight times the quantity of electricity dis- 
tributed over the surface of a single sphere of twice the 
radius (and, therefore, of twice the capacity, by Art. 272) 
of the original drops; and its electrical potential will 
therefore be four times as great. Xow a mass of cloud 
may consist of such charged spheroids, and its potential 
may gi-adually rise, therefore, by the coalescence of the 
drops, and the electrification at the lower surface of the 
cloud will become greater and greater, the surface of 
the earth beneath acting as a condensing plate and becom- 
ing charged, by influence, with the opposite kind of elec- 
trification. Presently the difference of potential becomes 
so great that the intervening strata of air give way under 
the strain, and a disruptive discharge takes place at the 
point where the air offers least resistance. This lightning y 
spark, which may be more than a mile in length, dis- 
charges only the electricity that has been accumulating 
at the surface of the cloud, and the other parts of the 
cloud will now react upon the discharged portion, pro- 
ducing internal attractions and internal discharges. The 
internal actions thus set up will account for the usual 
appearance of a thundercloud, that it is a well-defined 
flat-bottomed mass of cloud which appears at the top to 
be boiling or heaving up with continual movements. 

331. Lightning and Thunder. — Three kinds ' of 
lightning have been distinguished by Arago : (i.) The 
Zig-zag flash or '■^Forked lightning" of ordinary occur- 
rence. The zig-zag form is probably due either to the 



CHAP. IT LIGHTNING FLASHES 319 

presence of solid particles in the air or to local electrifi- 
cation at certain points, making the crooked path the one 
of least resistance, (ii.) Sheet lightning, in which whole 
surfaces are lit up at once, is probably only the reflexion 
on the clouds of a flash taking place at some other part 
of the sky. It is often seen on the horizon at night, 
reflected from a storm too far away to produce audible 
thunder, and is then known as "summer lightning." 
(iii.) Globular lightning, in the form of halls of fire, which 
move slowly along and then burst with a sudden ex- 
plosion. This form is very rare, but must be admitted 
as a real phenomenon, though some of the accounts of it 
are greatly exaggerated. Similar phenomena on a small 
scale have been produced (though usually accidentally) 
with electrical apparatus. 

The sound of the thunder may vary with the con- 
ditions of the lightning spark. The spark heats the air 
in its path, causing sudden expansion and compression 
all round, followed by as sudden a rush of air into the 
partial vacuum thus produced. If the spark be straight 
and short, the observer will hear but one short sharp clap. 
If its path be a long one and not straight, he will hear 
the successive sounds one after the other, with a charac- 
teristic rattle, and the echoes from other clouds will come 
rolling in long afterwards. The lightning-flash itself 
never lasts more than towo o ^f a second, but sometimes 
is oscillatory in character (see Art. 515). 

The damage done by a lightning-flash when it strikes 
an imperfect conductor appears sometimes as a disrup- 
tive mechanical disintegration, as when the masonry of a 
chimney-stack or church-spire is overthrown, and some- 
times as an effect of heat, as when bell-wires and objects 
of metal in the path of the lightning-current are fused. 
Th» physiological effects of sudden discharges are dis- 
cussed in Arts. 255 and 325. 

The *' return-stroke " experienced by persons in the 
neighbourhood of a flash is explained in Art. 29. 



320 ELECTRICITY AND MAGNETISM part ii 

332. Lightning Conductors. — The first suggestion 
to protect property from destruction by lightning was 
made by Franklin in 1749, in the following words : — 

" May not the knowledge of this power of points be of use to 
mankind, in preserving houses, churches, ships, etc., from the 
stroke of lightning, by directing us to fix on the highest parts of 
those edifices upright rods of iron made sharp as a needle, and 
gilt to prevent rusting, and from the foot of those rods a wire 
down the outside of the building into the ground, or round one of 
the shrouds of a ship, and down her side till it reaches the water ? 
Would not these pointed rods probably draw the electrical fire 
silently out of a cloud before it came nigh enough to strike, and 
thereby secure us from that most sudden and terrible mischief ? " 

Maxwell proposed to cover houses with a network of 
conducting wires, without any main conductor, the idea 
being that then the interior of the building will, like 
Faraday's hollow cube (Art. 34), be completely protected 
from electric force. Much controversy has arisen of late 
respecting lightning-rods. Professor Oliver Lodge main- 
tains the lightning flash to be of the nature of an electric 
oscillation (Art. 515) rather than a current. If so, the 
conductor of least resistance is not necessarily the best 
lightning-rod. Professor Lodge and the author inde- 
pendently, and for different reasons, recommend iron in 
preference to copper for lightning-rods. 

The following points summarize the modern views on 
the subject : — 

1. All parts of a lightning conductor should be of one and 
the same metal, avoiding joints as far as possible, and with as 
few sharp bends or corners as may be. 

2. The use of copper for lightning-rods is a needless extrava- 
gance. Iron is far better. Kibbon is slightly better than round 
rod; but ordinary galvanized iron telegraph-wire is good enough. 

3. The conductor should terminate not merely at the highest 
point of a building, but be carried to all high points. It is 
unwise to erect very tall pointed rods projecting several feet 
above the roof. 

4. A good deep ivet " earth " should be provided, independent 
of gas or water pipes, to which the conductor should be led down. 



CHAP. IV ATMOSPHERIC ELECTRICITY 321 

5. If in any part the conductor goes near a gas or water pipe 
it is better to connect them metallically than to leave them apart. 

6. In ordinary buildings the conductor should be insulated 
away from the walls, so as to lessen liability of lateral discharge 
to metal stoves and things inside the house. 

7. Connect all external metal-work, zinc spouts, iron crest 
ornaments, and the like, to each other, and to the earth, but 
not to the lightning conductor. 

8. The cheapest way of protecting an ordinary house is to 
run common galvanized iron telegraph-wire up all the corners, 
along all the ridges and eaves, and over all the chimneys ; tak- 
ing them down to the earth in several places, to a moist stratum, 
and at each place burying a load of coke. 

9. Over the tops of tall chimneys it is well to place a loop or 
arch of the lightning conductor, made of any stout and durable 
metal. 

333. Atmospheric Electricity. — In 1752 Lemomiier 
observed that the atmosphere usually was in an electrical 
condition. Cavallo, Beccaria, Ceca, and others, added 
to our knowledge of the subject, and more recently 
Quetelet and Lord Kelvin have generalized from more 
careful observations. The main result is that the air 
above the surface of the earth is usually, during fine 
weather, positively electrified, or at least that it is 
positive with respect to the earth's surface, the earth's 
surface being relatively negative. The so-called measure- 
ments of "atmospheric electricity" are really measure- 
ments of difference of potential between a point of the 
earth's surface, and a point somewhere in the air above it. 
In the upper regions of the atmosphere the air is highly 
rarefied, and conducts like the rarefied gases in Geissler's 
tubes (Art. 320). The lower air is, when dry, a non- 
conductor. The upper stratum is believed to be charged 
with -f- electricity, while the earth's surface is itself 
negatively charged ; the stratum of denser air between 
acting like the glass of a Leyden jar in keeping the 
opposite charges separate. If we could measure the 
electric potential at different points within the thickness 



322 ELECTRICITY AND MAGNETISM part ii 

of the glass of a charged jar, we should find that the 
values of the potential changed in regular order from a 
+ value at one side to a — value at the other, there being 
a point of zero potential aboufc half way between the two. 
Xow, the air in fine weather always gives + indications, 
and the potential of it is higher the higher we go to 
measure it. Cavallo found higher electrification just 
outside the cupola of St. Paul's Cathedral than at a lower 
point of the building. Lord Kelvin found the potential 
in the island of Arran to increase from 23 to 46 volts 
for a rise of one foot in level; but the difference of 
potential was sometimes eight or ten times as much for 
the same difference of level, and changed rapidly, as the 
east wind blew masses of cloud charged with + or — 
electricity across the sky. Joule and Kelvin, at Aber- 
deen, found the rise of potential to be equal to 40 volts 
per foot, or 1-3 volts per centimetre rise of level. 

During fine weather a negative electrification of the 
air is extremely rare. Beccaria only observed it six 
times in fifteen years, and then with accompanying 
winds. But in broken weather and during rain it is 
more often — than +, and exhibits great fluctuations, 
changing from — to +, and back, several times in haK 
an hour. A definite change in the electrical conditions 
usually accompanies a change of weather. '• If, when 
the rain has ceased (said Ceca), a strong excessive ( + ) 
electricity obtains, it is a sign that the weather will 
continue fair for several days." 

334. Methods of Observation. — The older observers 
were content to affix to an electroscope (with gold 
leaves or pith-balls) an insulated pointed rod stretch- 
ing out into the air above the ground, or to fly a kite, 
or (as Becquerel did) to shoot into the air an arrow com- 
municating with an electroscope by a fine wire, which 
Avas removed before it fell. Gay Lussac and Biot lowered 
a wire from a balloon, and found a difference of potential 
between the upper and lower strata of the air. Xone 



CHAP. IT ATMOSPHERIC ELECTRICITY 323 

of these methods is quite satisfactory, for they do not 
indicate the potential at any one point. To bring the 
tip of a rod to the same potential as the surrounding air, 
it is necessary that material particles should be dis- 
charged from that point for a short time, each particle 
as it breaks away carrying with it a + or a — charge 
until the potentials are equalized betvv'een the rod and 
the air at that point. Yolta did this by means of a small 
flame at the end of an exploring rod. Lord Kelvin has 
employed a " water-dropper," an insulated cistern pro- 
vided with a nozzle protruding into the air, from which 
drops issue to equalize the potentials : in winter he uses 
a small roll of smouldering touch-paper. Dellmann 
adopted another method, exposing a sphere to influence 
by the air, and then insulating it, and bringing it within- 
doors to examine its charge. Peltier adopted the kin- 
dred expedient of placing, on or near the ground, a 
delicate repulsion-electrometer, which during exposure 
was connected to the ground, then insulated, then re- 
moved indoors for examination. This process really 
amounted to charging the electrometer hy influence with 
electrification of opposite sign to that of the air. The 
" quadrant " electrometer, described in Art. 288, and a 
" portable " electrometer on the attracted-disk principle, 
are now used for observations on atmospheric electricity. 
Using a water-dropping collector and a Kelvin electro- 
meter, Everett made a series of observations in Nova 
Scotia, and found the highest + electrification in frosty 
weather, with a dry wind charged with particles of ice. 

335. Diurnal Variations. — Quetelet found that at 
Brussels the daily indications (during fine weather) 
showed twp maxima occurring in summer at 8 a.m. and 
9 P.M., and in winter at 10 a.m. and 6 p.m. respectively, 
and two minima which in summer were at the hours of 
3 P.M. and about midnight. He also found that in Janu- 
ary the electricity was about thirteen times as strong as 
in June. At Kew there is a maximum at 8 a.m. in 



324 ELECTRICITY AND MAGNETIS:\I pakt ii 

summer, and at 10 a.m. in winter; and a second mini- 
mum at 10 P.M. in summer and 7 p.m. in winter. The 
maxima correspond fairly with hours of changing tem- 
perature, the minima with those of constant temperature. 
In Paris, M. Mascart finds but one maximum, just before 
midnight : at sunrise the electricity diminishes until about 
3 P.M., when it has reached a minimum, whence it rises till 
nightfall. 

Our knowledge of this important subject is still very 
imx^erfect. We do not even know whether all the 
changes of the earth's electrification relatively to the air 
are due to causes operating above or below the earth's 
surface. Simultaneous observations at different places 
and at different levels are greatly wanted. 

336. The Aurora. — In all the northern regions of 
the earth the Aurora horealis, or "I^orthern Lights," is 
an occasional phenomenon ; and within and near the 
Arctic circle is of almost nightly occurrence. Similar 
lights are seen in the south polar regions of the earth, 
and are denominated Aurora australis. As seen in 
European latitudes, the usual form assumed by the 
aurora is that of a number of ill-defined streaks or 
streamers of a pale tint (sometimes tinged with red and 
other colours), either radiating in a fan-like form from 
the horizon in the direction of the (magnetic) north, or 
forming a sort of arch across that region of the sky, 
of the general form shown in Fig. 169. A certain flick- 
ering or streaming motion is often discernible in the 
streaks. Under very favourable circumstances the au- 
rora extends over the entire sky. The appearance of 
an aurora is usually accompanied by a magnetic storm 
(Art. 159), affecting the compass-needles over whole 
regions of the globe. This fact, and the position of the 
auroral arches and streamers with respect to the 
magnetic meridian, directly suggest an electric origin 
for the light, — a conjecture which is confirmed by the 
many analogies found between auroral phenomena and 



THE AtJRORA 



B21 



those of discharge in rareiied. air (Arts. 320 and 322). 
Yet the presence of an aurora does not, at least in our 
Latitudes, affect the electrical conditions of the lower 
regions of the atmosphere. On September 1, 1859, a 
severe magnetic storm occurred, and auroras were 
observed almost all over the globe ; at the same time 





Fig. 169. 



a remarkable outburst of energy took place in the 
photosphere of the sun; but no simultaneous develop- 
ment of atmospheric electricity was recorded. Aurorte 
appear in greater frequency in periods of about 11^- 
years, which agrees pretty well with the cycles of 
maximum of magnetic storms (see Art. 159) and of 
sun-spots. 



326 ELECTRICITY AND MAGNETISM part ii 

The spectroscope shows the auroral light to be due 
to gaseous matter, its spectrum consisting of a few bright 
lines not referable with certainty to any known terrestrial 
substance, but having a general resemblance to those 
seen in the spectrum of the electric discharge through 
rarefied dry air. 

The most probable theory of the aurora is that origi- 
nally due to Franklin ; namely, that it is due to electric 
discharges in the upper air, in consequence of the differ- 
ing electrical conditions between the cold air of the polar 
regions and the warmer streams of air and vapour raised 
from the level of the ocean in tropical regions by the 
heat of the sun. 

According to Xordenskiold the terrestrial globe is 
perpetually surrounded at the poles with a ring or cro^m 
of light, single or double, to which he gives the name of 
the " aurora-glory." The outer edge of this ring he esti- 
mates to be at 120 miles above the earth's surface, and 
its diameter about 1250 miles. The centre of the aurora- 
glory is not quite at the magnetic pole, being in lat. 81° 
'N., long. 80° E. This aurora-glory usually appears as a 
pale arc of light across the sky, and is destitute of the 
radiating streaks shown in Fig. 169, except during 
magnetic and auroral storms. 

An artificial aurora has been produced by Lemstrom, 
who erected on a mountain in Lax3land a network of 
wires presenting many points to the sky. By insulating 
this apparatus and connecting it by a telegraph-wire with 
a galvanometer at the bottom of the mountain, he was 
able to observe actual currents of electricity when the 
auroral beam rose above the mountain. 



CHAPTER V 

ELECTROMAGNETICS 

Lessox XXVT. — Magnetic Potential 

337. Electromagnetics. — That, branch of the science 
of electricity which treats of the relation between elec- 
tric currents and magnetism is termed Electromagnetics. 
In Arts. 128 to 140 the laws of magnetic forces were 
explained, and the definition of "unit pole" was given. 
It is, however, much more convenient, for the purpose of 
stud}^, to express the interaction of magnetic and electro- 
magnetic systems in terms not of "force" but of '■'■poten- 
tial" ; i.e. in terms of their power to do work. In Art. 
263 the student was shown how^ the electric potential due 
to a quantity of electricity may be evaluated in terms of 
the work done in bringing up as a test charge a unit of 
+ electricity from an infinite distance. Magnetic poten- 
tial can be measured similarly by the ideal process of 
bringing up a unit magnetic pole (IST-seeking) from an 
infinite distance, and ascertaining the amount of work 
done in the operation. Hence a large number of the 
points proved in Lesson XXI. concerning electric poten- 
tial will also hold true for magnetic potential. The 
student may compare the following propositions with the 
corresponding ones in Articles 263 to 268: — 

(a) The magnetic potential at any point is the K'orl' that 
must be spent upon a unit magnetic (X-seekiiig) 
327 



328 ELECTRICITY AND MAGNETISM part n 

pole in hring'ing it up to that point from an infinite 
distance. 

(b) The magnetic jjotential at any point due to a system 
of magnetic poles is the sum of the separate magnetic 
potentials due to the separate poles. 

The student must here remember that the potentials 
due to S-seeking poles Avill be ot opposite sign to those 
due to X-seeking poles, and must be reckoned as negative. 

(c) 77ie {magnetic') potential at any point due to a system 
of magnetic poles may he calculated (compare with 
Art. 283) hy summing up the strengths of the sep- 
arate poles divided each by its own distance from 
that point. Thus, if poles of strengths m', m", 
m'", etc., be respectively at distances of ?-', ?'", r'", 
. . . from a point P, then the following equa- 
tion gives the potential at P : — 



nv _^ m" m'" 



or \ p = 2 - 



(d) The difference of (inagnetic') potential between two 
points is the loork to be done on or by a unit 
(X-seeking) pole in moving it from one point to the 
other. It follows that if m units of magnetism 
are moved through a difference of potential V. the 
work AV done will be 

W = mX. 

(e) Magnetic force on unit pole is the rate of change 
of (inagnetic) p>otential per unit of length: it is 
numerically equal to the intensity of the field. 
Since by Art. 141, 

f=mn, 

and work is the product of a force into the length 



CHAP. V MAGNETIC POTENTIAL 329 

through which its point of application moves for- 
ward, it follows that 

W =/ = mm. 
But 

W = mV; 
whence 

Y = HZ, 
and 

H = \/l. 

Example. — The difference of magnetic potential between two 
points 5 centims. apart along a magnetic field in wliich there 
are 6000 lines per sq. cm., is 30,000. Or, it would require 
30,000 ergs of work to be expended to pusli a unit pole from 
one point to the other against the magnetic force. 

(f) Equipotential surfaces are those (imaginary) surfaces 
surrounding a magnetic pole or sijstem of poles, over 
lohich the (magnetic) potential has equal values. 
Thus, around a single isolated magnetic pole, the 
potential would be equal all round at equal dis- 
tances ; and the equipotential surfaces would be 
a system of concentri<3 spheres at such distances 
apart that it would require the expenditure of one 
erg of work to move a unit pole up from a point 
on the surface of one sphere to any point on the 
next (see Fig. 146). Around any real magnet 
possessing two polar regions the equipotential sur- 
faces would be much more complicated. Magnetic 
force., whether of attraction or repulsion, ahcays acts 
across the equipotential smfaces in a direction nor- 
mal to the surface; the magnetic lines of force are 
everywhere perpendicular to the equipotential su7'- 
faces. 

Flux of Force. — From a single magnetic pole (sup- 
posed to be a point far removed from all other poles) the 
lines of force diverge radially in all directions. The 
space around may be conceived as thus divided up into 



330 ELECTRICITY AND MAGNETISM part ii 

a number of conical regions, each having their apex at 
that pole; and through each cone, as through a tube, 
a certain number of lines of force will pass. Such a 
conical space may be called a " tube " of force. The 
total number of magnetic lines within any tube of force 
is called the magnetic flux.* l^o matter where you cut 
across a tube of force, the cross-section will cut through 
the enclosed flux, though the lines diverge more widely 
as the tube widens. Hence, 

(g) Tlie magnetic flux across any section of a tube of 
force is constant wherecer the section he taken. 

In case the magnetism is not concentrated at one 
point, but distributed over a surface from which the 
tubes start, we shall have to speak of the " amount of 
magnetism " rather than of the " strength of pole," and 
in such a case the 

(h) Magnetic density is the amount of magnetism per 
unit of surface. In the case of a simple magnetic 
shell over the face of which the magnetism is 
distributed with uniform density, the " strength " 
of the shell will be equal to the thickness of 
the shell multiplied by the surface-density. 

338. Intensity of Field. — We have seen (Art. 11.5) 
that every magnet is surrounded by a certain "field," 
within which magnetic force is observable. We may 
completely specify the properties of the field at any 
point by measuring the strength and the direction of that 
force, — that is, by measuring the " intensity of the field " 
and the direction of the lines of force. The " intensity of 
the field " at any point is measured by the force with which 
it acts on a unit pole placed at that jjoint. Hence, ujiit 
intensity of field is that interisity of field which acts on a unit 
pole icith a force of one dyne. There is therefore a field of 

* The magnetic flux is bj' some writers called the total induction ; 
but the word induction ought to be kept for the operation of inducing. 



CHAP. V LINES IN MAGNETIC FIELD 331 

unit intensity at a point one centimetre distant from the 
pole of a magnet of miit strength. Suppose a magnet 
pole, whose strength is ??;, placed in a field at a point 
where the intensity is H, then the force will be ?n times 
as great as if the pole were of unit strength, and 

/= m X H. 

To aid the imagination by a graphic conception we 
adopt Faraday's notion of representing the properties of a 
magnetic field by supposing lines to be drawn so that 
they represent the direction and intensity of the field by 
the direction and density of the lines. This leads to the 
empirical rule to draw as many magnetic lines to the 
square centimetre (of cross section) as there would be 
dynes of force on unit pole. A field of H units means 
one where there would be H dynes on unit pole, or H 
lines per square centimetre. It follows that a unit mag- 
netic pole will have 47r lines of force proceeding from it: for 
there is unit field at unit distance away, or one magnetic 
line per square centimetre ; and there are 47r square 
centimetres of surface on a sphere of unit radius drawn 
round the pole. A magnet, whose pole-strength is m, has 
4:7rm, or 12-57 x m, lines running through the steel, and 
diverging at its pole. The above-mentioned rule is the 
origin of the 47r symbol which comes in so often into 
electromagnetic formulae. Suppose a narrow crevasse 
between the faces of two opposing magnets, each having cr 
units of magnetism per square centimetre of their pole 
surfaces. The field in the space between will have the 
value 

H = 47ro-. 

339. Work done by Conductor carrying Current 
when it cuts across the Lines of a Magnetic Field. — 
By definition (Art. 263) it follows that tlie work W 
done in moving Q units of electricity against an electro- 
motive-force V is equal to QV. Suppose that this electro- 



332 ELECTRICITY AND MAGNETISM part ii 

motive-force is due to the conductor cutting N magnetic 
lines during time t. Then if the motion be uniform and 
the average current during the time is called C, it follows 
that Q = Ct. And the average electromotive-force is (see 
Art. 225) = "N/t. Inserting these values we get 

W =: C^ X N/^, 
or W = CN ; 

or, in words, the work done in moving a current across a 
magnetic Jlux is equal to the product of the current into the 
total number of magnetic lines cut. It will be noted that 
the work is the same whether the time is long or short. 
If C and N are in absolute (C.G.S.) units, W will be iii 
ergs. 

340. Force exerted by Magnetic Field on Wire carry- 
ing Current. — If a wire is moved sidewa3^s across the 
lines of a magnetic field, through a distance x it will 
sweep out an area equal to its own length Z multiplied 
by X. And if H is the number of magnetic lines per 
square centimetre the total number of lines cut will be 
= B.lx ; and the work done if the wire carries current 
C will be = CRlx. But if work W is done in moving the 
wire through distance x the force / exerted will be W /x. 
Hence the force on the wire will be 

f^CEl; 

or, in words, the force is proportional to the current, to 
the intensity of the field, and to the length of wire in the 
field. It is a force that tends to drag the wire laterally, 
acting at right angles to the wire and to the lines of the 
field. ■ 

This action is of course due to stresses going on in the 
medium, and is worthy of further thought. Consider 
the magnetic field in a gap between a large N-pole and 
a similar S-pole. The lines will go nearly uniformly 
straight across. Let a current flow in a copper wire that 
lies across the field. In Fig. 170 the wire is seen end- 



MxVGXETOMOTIVE FORCE 



333 



ways, with the cm-rent flowmg " up " or toward the 

observer. The result will be that the magnetic field of 

the current (Art. 202) will be superposed upon that of 

the magnets, and will 

perturb it : the form 

of the perturbed field 

being that shown. In 

such a field the stresses, 

which act as though 

the magnetic lines 

tended to shorten 

themselves, will have 

the effect of urging the 

wire mechanically in 

the direction shown. 

This mechanical force 

acts on the matter of 

the wire, though due 

to the current. 

In calculating by 
the expression above, if C is given in amperes it must be 
divided by 10. 

341. Magnetomotive-force (or Total Magnetizing 
Force) of a Current circulating in a Spiral Conductor. — 
Let a conductor carrying a current of C amperes be coiled 
up in a spiral having S as the number of turns. It is 
known, and easily understood, that the total magnetizing 
force of such is propoi-tional to the number of ampere- 
turns ; for experiment shows that, for example, a current 
of 10 amperes circulating in a coil of 50 turns has pre- 
cisely the same magnetic power as a current of 5 amperes 
in 100 turns, or as a current of 1 ampere in 500 turns. 
Each of these has 500 ampere-turns. 

To obtain the full expression let us find the work that 
would be done in the act of moving a unit magnet-pole 
around any closed path (Fig. 171) from any point P to 
the same point again, such path passing through all the 




334 ELECTRICITY AXD MAGNETISM pakt ii 

turns of the magnetizing coil. The work done on a unit 

pole in moving it once around the closed path, against 

the magnetic forces of the system, is a measure of the 

power of that system to magnetize : or, in other words, is a 

measure of its magnetomotive-force. Such a closed path 

may lie, according to circumstances, either wholly in air, 

or partly in air partly in iron, or wholly 

-=:t>-yYYy^ ^^^ iron. The argument is entirely in- 

/'UU 0'uO"\ dependent of any materials lying along 

'v._ _.,,.'' the ideal path. 

Yig, 171. Xow imagine this unit-pole, with its 

4:TT magnetic lines radiating out of it, to 
be passed along the closed path (Fig. 171) from P, through 
the spirals to P again. Each turn of the coil will cut each 
of the magnetic lines once, and therefore, by Arts. 338 
and 339, the total work done will be 

W = 47rCS/10, 

where we divide by 10 to bring amperes to C.G.S. miits. 
Or, since 47r = 12-57, we get the rule — the magnetomotive- 
force* of a coll is equal to 1-257 times the amjjere-turns. 

342. Intensity of Field in a Long Tubular Coil, or 
Solenoid. — A spiral coil wound on a tube is called a 
solenoid. It has, when a current circulates in its coils, 
a magnetic field along the inside of it, and is, in 
fact, so long as the current cumulates, a magnet without 
iron. This magnetic field, if the spiral is a very long one 
— say 20 times as long as the diameter of the spirals, — 
is very uniform all along the interior, except just toward 
the ends, where it becomes weaker. To find the intensity 
of the field H, we may remember that (Art. 337 e) the 
work done on a unit-pole in moving it through a length 
I of field H is equal to Bl. But the work done in 

* Since this magnetomotive-force is made up of a number of small 
elements distributed variously along the path it is sometimes called the 
line-integral of the magnetizing forces. 



CHAP. V FIELD DUE TO CURKENT 335 

moving it along the tubular coil of length I is practically 
equal to that doue around the closed path, since nearly 
all the forces are met along the part of the path inside. 
Hence we may equate -IttCS/IO to HZ; giving the result 

10 I ' 

or the intensity of the Jield in a long spiral is equal to 1-257 
times the number of ampere-turns jJer centiinetre of length. 

At the mouth of a long spiral the intensity of the field 
is exactly half what it is midway between the ends. 

343. Magnetic Field due to Indefinitely Long Straight 
Current. Law of Inverse Simple Distance. — Consider a 
unit-pole at point P at a distance r (Fig. 
172) from an indefinitely long straight con- 
ductor carrying a current of C amperes. 
The force tending to make the pole circulate 
around the wire may be calculated very sim- 
ply as follows. If the unit-pole were to be 
moved once around the wire on a circular 
path with radius r, each one of the ^tt mag- 
netic lines that radiate from it would be cut 
once by the wire. Hence, by Art. 339, the 
work done in one such revolution would be lig-lf2. 
equal to 47rC/10. But this work has been done by mov- 
ing the unit, against the forces of the system, along a 
path the length of which is 27rr; wherefore 

W =/x 27rr = 47rC/10, 
whence 

/=2C/10r. 

From this it appears that the force on unit-pole, and 
therefore the intensity of the field, is directly proportional 
to the current, and varies inversely as the simple distance 
from the wire. 

Example. — The force exerted on a pole of 1200 units of 



?P 



336 ELECTRICITY AND MAGNETISM part ii 

magnetism at a distance of 4 centimetres from a long 
straight wire carrying current of 60 amperes will be 3G0O 
dynes, or 3'52 grammes. 

The fact that the force varies inversely as the simple 
distance, and not as the square, was experimentally 
discovered by Biot and Savart in 1820. 

Around such a straight conductor the magnetic field 
consists of a cylindrical whirl of circular lines (Art. 202), 
their density decreasing as their radius increases. Outside 
a straight wire carrying a 10 ampere current the values of 
Hare: 2 at 1 cm.; 1 at 2 cm.; 0-4 at 5 cm., and so 
forth. The pole tends to move circularly around the 
wire. 

344. Mutual Action of Magnet-pole and of Element 
of Current. — Consider an element of current, that is to 

say, an indefinitely short piece 

I of a conductor traversed by a 

current. Calling the length dl, 

^l and the current C, we have Cof/ 

as the magnetic value of the 

I element with respect to all 

Pi^ Yi'i points in its equatorial plan. 

Suppose the element to be set 

(Fig, 173) at distance r from a magnet-pole of m units, 

and at right angles to the line joining them. Then, 

as the element is small compared with ?% the law of 

inverse squares will hold good : the mutual force will be 

r _ m-Cdl ^ 
J- iot2* 

This will be neither an attraction nor a repulsion, but a 
force at right angles to the element and to the line join- 
ing it to m. 

345. Magnetic Field due to Circular Current. — It 
is desired to find the effect of a circular current (Fig. 
174) at any point on the axis, at a distance x from the 
centre. Suppose a unit-pole were placed at this point 




CHAP. T FIELD OF CIKCULAR COIL 387 

P. only a fraction of the -Itt lines which radiate from it 
■will pass through the circle ; the number being propor- 
tional to the solid-angle (Art. 1-18) 
subtended at P by the circle, namely 
'2-77 (1 — cos 0), where is the angle 
between axis and slant distance a. 
Hence in bringing up the pole to this 
place, from an infinite distance, the 
work done by causing these lines to Fig. 174. 

cut across the wire carrying current C amperes will be 
(by Art. 339) 

W = 27rC(l -cos(9)/10. 

This represents the mutual energy of pole and current. 
To calculate the force at P we must differentiate this 
expression with respect to x, to ascertain the rate at which 
the mutual energy falls per unit length. For this purpose 
it will be convenient to substitute for cos 6 its value 

x/(x^ + ?/2)2. Substituting and differentiating we get 

f= d\Y/dx =T%7rC//(:.2 + ^-2)1 

Now {x^ + ?/2)2 is equal to a^; whence the rule that the 
magnetic force at any point P on the axis varies directly 
as the current, and inversely as the cube of the slant distance. 
(Compare case of a bar-magnet. Art. 138.) 

Another way of arriving at this result is as follows. 
Taking the expression found in Art. 344 for the action of 
an element of current, we may consider the effect of the 
topmost element of the ring (Fig. 174), situated at a 
slant distance a = Vx"^ + y^. The elementary force df 
exerted on unit-pole at P by the element Cdl will be at 
right angles to a and to dl (in direction of the arrow), 
and, by Art. 206, of the value 

df = Cdl/ 10 a^. 

As the elements such as dl are symmetrical around the 
axis we must resolve their oblique forces into two parts ; 
z 



338 ELECTRICITY AND MAGNETISM part ii 

part acting at right angles to the axis, which will dis- 
appear by mutually cancelling out in pairs, and part 
acting in the line of the axis, which will for each element 
be equal to the above expression multiplied by sin 6. So 
that the elementary axial force due to each element of 
length dl will be 

df= Cdl • sin^/ioa^; 

or, since sin = y/a, 

df=Cdl-yoi/a^. 

But the total force /due to all the elements will be the 
integral due to the sum of their lengths, and this integral 
length around the circle h/dl = '27r}j. Whence it at once 
follows that 

f=27rCi//ioa^. 

Note that if P is pushed up to the centre of the circle 
a = y, and we get back to the rule for tangent galva- 
nometer (Art. 212),/= 27rC/ior. 

Also note that for very great distances of P from 
centre a becomes sensibly equal to x, the force varying 
inversely as the cube of the axial distance. 

This affords one way of varying the sensitiveness of 
tangent galvanometers, the needle with its scale being 
arranged to slide out along the axis of the coil. At a 
point P, such that a = 2y, the force of coil on needle is 
only I of what it is at centre. 

346. Moment of Circular Coil. — A circular coil carry- 
ing a current acts as a magnet whose axis is the axis 
of the coil. Its magnetic moment (Art. 135) will be the 
product of the current (in absolute units) into the area 
enclosed. Or, if C is in amperes, and A the total area 
of all the turns, its moment will be AC/ 10. If such a 
coil is placed in a field of intensity H it will tend to 
turn so as to place its axis along the direction of the field. 
If the angle between those directions is ^ the torque (or 
turning-moment) \\i\] be = ACH sin 6/10, 



CHAP. V POTENTIAL OF MAGNETIC SHELL 



339 



347. Potential due to a Solenoidal or Circuital Distribution 
of Magnetism. — A long thin uniformly magnetized magnet 
exhibits poles only at the two ends, and acts on external objects 
just as if there were two equal quantities of opposite kinds of 
magnetism collected at these two points. Such a distribution 
of magnetism is sometimes called solenoidal or circuital. The 
magnetic potential due to a solenoid, and all its magnetic 
effects, depend only on the position of its two poles, and on 
their strength, and not on the form of the bar between them, 
whether straight or curved. In Art. 337 (c) was given the rule 
for finding the potential due to a system of poles. Suppose the 
two poles of a solenoid have strengths + m and — m respectively, 
and that the distances of these poles from an external point P 
are ri and r-i, then the potential at P will be 

1 1 



Vp 



Suppose a magnet curled round until its N and S poles touch 
one another : it will not act as a magnet on an external object, 
and will have no "field"; for if the two poles are in contact, 
their distances r^ and r.2 to an external point P will be equal, and 

- — -Willie = 0. 
"1 r.2 1 

348. Potential due to a Magnetic Shell. — Gauss demon- 
strated that the potential due to a magnetic shell at a point near 
it is equal to the strength of the shell multiplied hy the solid-angle 
subtended by the shell at that point ; the " strength " of a magnetic 
shell being the product of its 

thickness into its surface- ,P 

density of magnetization. 

If w represents the solid- 
angle subtended at the point 
P, and i the strength of the 
shell, then 



Vp 




Fiff. 1' 



Proof. — To establish this 
proposition would require the 

integral calculus. But the following geometrical demonstration, 
though incomplete, must here sufitice. 

Let us consider the shell as composed, like that drawn, of a 
series of small elements of thickness t, and having each an area 
of surface s. The whole solid-angle subtended at P by the shell 



340 ELECTRICITY AND MAGNETISM part ii 



may likewise be conceived as made up of a number of elementary 
small cones, each of solid-angle (^ : Let j\ and r.2 be the distances 
from P to the two faces of the element : Let a section be made 
across the small cone orthogonally, or at right angles to j\, and 
call the area of this section a : Let the angle between the sur- 
faces s and a be called angle |8: then s = a/cos ^. Let i be the 
" strength " of the shell (i.e. = its surface-density of magnetism 
X its thickness) ; then i/t = surface-density of magnetism, and 
si/t = strength of either pole of the little magnet — m. 

^^ .. , , area of its orthogonal section 
Now solid-angle u = -^ 

= a/f^ ; 
therefore a = ^r'^, 

and 5 = '^7'2/cosi3. 

Hence wirV^ cos fi = ni. 

But the potential at P of the magnet whose pole is m will be 



1 1 1^2 ~ '>'! ^'2 ~ ''l 

^^* ^~^^ r^r.2 ' ^'^^^"^^ ^® "^^y ^'"^® -^— 

because Vi and ?'2 r>iay be made as nearly equal as we please. 
And since r.2 — )'i = t cos ^ 



r2 ft cos p\ 
^ = •^^^55^ [-r^-J 



or the potential due to the element of the shell = the strength 
of the shell x the solid-augle subtended by the element of the 
shell. Hence, if V be the sum of all the values of v for all the 
different elements, and if w be the whole solid-angle (the sum 
of all the small solid-angles such as c6) , 

Yv = u>i, 
or the potential due to a magnetic shell at a point is equal to 
the strength of the shell multiplied by the solid-angle subtended 
by the whole of the shell at that point. 

Hence wi represents the work that would have to be done on or 
by a unit-pole, to bring it up from an infinite distance to the point 
P, where the shell subtends the solid-angle w. At a point Q 



CHAP. V POTENTIAL OF MAGNETIC SYSTEM 341 



where the solid-angle subtended by the shell is different, the 
potential will be different, the difference of potential between 
P and Q being 

Vy — Yp = i (wq — wp) . 

If a magnet-pole whose strength is m were brought up to P, 
m times the work would have to be done, or the mutual poten- 
tial would be — niiai. 

349. Potential of a Magnet-pole on a Shell.— It is evi- 
dent that if the shell of strength i is to be placed where it 
subtends a solid-angle w at the pole m, it would require the 
expenditure of the same amount of work to bring up the shell 
from an infinite distance on the one hand, as to bring up the 
magnet-pole from an infinite distance on the other; hence niwi 
represents both the potential of the pole on the shell and the 
potential of the shell on the pole. Now the lines of force from a 
pole may be regarded as proportional in number to the strength 
of the pole, and from a single pole they would radiate out in all 
directions equally. Therefore, if a magnet-pole was j)laced at P, 
at the apex of the solid-angle of a cone, the number of lines of 
force which would pass through the solid-angle would be propor- 
tional to that solid-angle. It is therefore convenient to regard 
moi as representing the number of lines of force of the pole which 
pass through the shell, and we may call the number so inter- 
cepted N. Hence the potential of a magnet-pole on a mag- 
netic shell is equal to the strength of the shell multiplied by the 
number of lines of force (due to the magnet-pole) which pass 
through the shell ; or Y = Ni. If either the shell or the pole 
were moved to a point where a different number of lines of force 
were cut, then the difference of potential would be 

Vq-Yp = ±z (Nq-Np). 
To bring up a N-seeking (or +) pole against the repelling 
force of the N-seeking face of a magnetic shell requires a posi- 
tive amount of work to be done ; and their mutual reaction 
would enable work to be done afterwards by virtue of their 
position: in this case then the potential is +. But in moving a 
N-seeking pole up to the S-seeking face of a shell work will be 
done by the pole, for it is attracted up ; and as work done by 
the pole may be regarded as our doing negative work, the 
potential here will have a negative value. 

Again, suppose we could bring up a unit N-seeking pole 
against the repulsion of the N-seeking face of a shell of strength 
i, and should push it right up to the shell ; when it actually 
reached the plane of the shell the shell would occupy a whole 



342 ELECTRICITY AND MAGNETISM part ii 



horizon, or half the whole space around the pole, the solid-angle * 
it subtended being therefore 2n, and the potential will be + 27ri. 
If we had begun at the S-seeking face the potential at that face 
would be — 27ri. It appears then that the potential alters its 
value btj ^iri on passing from one side of the shell to the other. 

There is a reaction between pole and shell similar to that 
(Art. 121) between pole and pole. 

If a N-seeking pole be brought up to the N-seeking face of a 
shell none of the lines of force of the magnet will cut the shell, 
but will be repelled out as in Fig. 72 ; whereas if a N-seeking pole 
be brought up to the S-seeking face of a shell, large numbers of 
the lines will be run into one another ; and the pole, as a matter 
of fact, will be attracted up to the shell, where as many lines of 
force as possible are cut by the shell. We may formulate this 
action by saying that a magnetic shell and a magnet-pole react 
on one another and urge one another in such a direction as 
to make the numher of lines of force that are cut by the shell a 
maximum (Maxwell's Rule, Art. 201). Outside the attracting 
face of the shell the potential is -co/, and the pole moves so as to 
make this negative quantity as great as possible, or to make the 
potential a minimum. Which is but auother way of putting the 
matter as a particular case of the general proposition that bodies 
tend to move so that the energy they possess in virtue of their 
position tends to run down to a minimum. 

350, Magnetic Potential due to Current. — The proposi- 
tions concerning magnetic shells given in the preceding para- 
graphs derive their great importance because of the fact laid 
down in Art. 203 that circuits, traversed by currents of electri- 
city, behave like maguetic shells. Adopting the electromagnetic 
unit of current (Art. 353), we may at once go back to Art. 347, 
and take the theorems about magnetic shells as being also true 
of closed voltaic circuits. 

(a) Potential due to closed circuit (compare Art. 348). 

The potential V due to a closed voltaic cii'cuit (traversed by 
a current) at a point P near it, is equal to the strength of the 
current multiplied by the solid-angle w subtended by the circuit 
at that point. If C be the strength of the current in electro- 
magnetic units, then 

Vp = -coC. 

(6) At a point Q, where the solid-angle subtended by the 
circuit is wq instead of wp, the potential will have a different 
value, the difference of potential being 

Vq-^^p = -CK--p)- 

* See note on Ways of Reckoning Angles, Art. 144 and Appendix A. 



CHAP. V MUTUAL POTENTIAL 343 



(c) Mutual Potential of a Magnet-pole and a Circuit. — If 
a magnet-pole of strength rn were brought up to P, m times as 
much 'U'ork will be done as if the maguet-pole had been of unit 
strength, and the work woukl be just as great whether the pole 
m were brought up to the circuit, or the circuit up to the pole. 
Hence, the mutual potential will be 
— nic^C. 
But, as in Art. 349, we may regard in<^ as representing the 
number of lines of force of the pole which are intercepted by 
and pass through the circuit, and we may write N for that num- 
ber, and say 

V = - CN, 

or the mutual potential of a magnet-pole and a circuit is equal 
to the strength of the current multiplied by the number of the 
magnet-pole's lines of force that are intercepted by the circuit, 
taken with reversed sign. 

{d) As in the case of the magnetic shell, so with the circuit, 
the value of the potential changes by iirC from a point on one 
side of the circuit to a point just on the other side; that is to 
say, being — 2 ttC on one side and + 2 ttC on the other side work 
equal to 4 ttC must be done in carrying a unit-pole from one side 
to the other round the outside of the circuit. The work done in 
thus threading the circuit along a path looped S times round it 
would be 4 7rSC. 

351. {e) Mutual Potential of two Circuits. — Two closed 
circuits will have a mutual potential, depending on the strengths 
of their respective currents, on their distance apart, and on their 
form and position. If their currents be respectively C and C, 
and if the distance between two elements ds and ds' of the cir- 
cuits be called r, and e the angle between the elements, it can be 

shown that their mutual potential is = — CC l \ —^ ds ds' . 

This expression represents the work that would have to be done 
to bring up either of the circuits from an infinite distance to its 
present position near the other, and is a negative quantity if they 
attract one another. Now, suppose the strength of current in 
each circuit to be unity; their mutual potential will in that 

C /^COS e 

case be i i ds ds' , a quantity which depends purely upon 

the geometrical form and position of the circuits, and for which 
we may substitute the single symbol M, which we will call the 
" coefficient of mutual potential " : we may now write the mutual 
potential of the two circuits when the currents are C and C as 
= -CC'M. 



344 ELECTRICITY AND MAGNETISM part ii 



But we have seen in the case of a single circuit that we may- 
represent tlie potential between a circuit and a unit-pole as the 
product of the strength of the current — C into the number N of 
the magnet-pole's lines of force intercepted by the circuit. Hence 
the symbol M must represent the number of each other's lines of 
force mutually intercepted by both circuits, if each carried unit 
current. If we call the two circuits A and B, then, when each 
carries unit current, A intercepts M lines of force belonging to 
B, and B intercepts M lines of force belonging to A. 

Now suppose both currents to ruu in the same (clock-wise) 
direction ; the front or S-seeking face of one circuit will be 
opposite to the back or N-seeking face of the other circuit, and 
they will attract one another, and will actually do work as they 
approach one another, or (as the negative sign shows) negative 
work will be done in bringing up one to the other. When 
they have attracted one another up as much as possible the cir- 
cuits will coincide in direction and position as nearly as can ever 
be. Their potential energy will have run down to its lowest 
minimum, their mutual potential being a negative maximum, 
and their coefficient of mutual potential M, having its greatest 
possible value. Two circuits, then, are urged so that their 
coefficient of mutual potential M shall have the greatest possible 
value. This justifies Maxwell's Rule (Art. 20i), because M 
represents the number of lines of force mutually intercepted 
by both circuits. And since in this position each circuit induces 
as many lines of magnetic force as possible through the other, 
the coefficient of mutual potential M is also called the coeffi- 
cient of mutual induction (Art. 454). 

Lessox XXYII. — The Electromagnetic System of Units 

352. Magnetic Units. — All magnetic quantities, strength 
of poles, intensity of magnetization, etc., are expressed in terms 
of special units derived from the fundamental units of length, 
mass, and time, explained in the Note on Fundamental and 
Derived Units (Art. 280). Most of the following units have 
been directly explained in the preceding Lesson, or in Lesson 
XL ; the others follow from them. 

Unit Magnet-pole. — The unit magnetic pole is one of such 
a strength, that when placed at a distance of 1 centi- 
metre (in air) from a similar pole of equal strength, 
repels it with a force of 1 dyne (Art. 141) . 
Magnetic Potential. — Magnetic potential being measured 
by work done in moving a unit magnetic pole against the 



ELECTROMAGNETIC UNITS 345 



magnetic forces, the unit of magnetic potential will be 
measured by the unit of work done on unit-pole. 

Unit Difference of Magnetic Potential. — Unit difference of 
magnetic potential exists between two points when it 
requires the expenditure of one erg of work to bring a 
(N-seeking) unit magnetic pole from one point to the 
other against the magnetic forces. Magnetomotive-force, 
or magnetizing poAver, is measured in same units as 
difference of magnetic potential. 

Intensity of Magnetic Field is measured by the force it 
exerts upon a unit magnetic pole : hence, 

Unit Intensity of Field is that intensity of field which acts 
on a unit (N-seeking) pole with a force of 1 dyne. The 
name of gauss has been proposed for this unit. A field 
having an intensity of 6000 lines per square centimetre 
would be described as 6 kilogausses. 

Magnetic Flux, or total induction of magnetic lines, is 
equal to intensity of field multiplied by area. Its unit 
will be one magnetic line. 

Magnetic Reluctance (see Art. 376) is the ratio of magneto- 
motive-force to magnetic flux. Unit reluctance will be 
such that unit magnetomotive-force generates in it a 
flux of one line. 

353. Electromagnetic Units. — The preceding magnetic 
units give rise to the following set of electrical units, in which 
the strength of currents, etc., are expressed in magnetic ineasure. 
They are sometimes called " absolute C.G.S." units. The relation 
of this "electromagnetic" set of units to the "electrostatic" 
set of units of Art. 283 is explained in Art. 359. 

Unit Strength of Current. — A current has unit strength when 
one centimetre length of its circuit bent into an arc of 
one centimetre radius (so as to be always one centimetre 
away from the magnet-pole) exerts a force of one dyne 
on a unit magnet-pole placed at the centre (Art. 207). 

Unit of Difference of Potential (or of Electromotiveforce). 
— Potential is work done on a unit of electricity; hence 
unit difference of potential exists between two points 
when it requires the expenditure of one erg of work to 
bring a unit of + electricity from one point to the other 
against the electric force. Also, unit electromotive-force 
is generated by cutting one magnetic line per second. 

Unit of Resistance. — A conductor possesses unit resistance 
when unit difference of potential between its ends causes 
a current of unit strength to flow through it. 



346 ELFXTRICITY AND MAGNETISM part ii 



Unit of Quantity of Electricity is that quantity which is 

conveyed by unit current in one second. 
Unit of Capacity. — Unit capacity requires unit quantity to 

charge it to unit potential. 
Unit of Induction. — Unit induction is such that unit 

electromotive-force is induced by the variation of the 

current at the rate of one unit of current per second. 

354. Practical Units and Standards.*— Several of the 
above " absohite " units in the C.G.S. system would be incon- 
veniently large and others inconveniently small for practical 
use. The following are therefore chosen as practical units: — 

Resistance. — The Ohm, = lO^ absolute units of resistance 
(and theoretically the resistance represented by the 
velocity of one earth-quadrant per second, see Art. 357), 
but actually represented by the resistance of a uniform 
column of mercury 106'3 centimetres long and 14:'4521 
grammes in mass, at 0^ C. Such a column of mercury is 
represented by a " standard " ohm (see Appendix B). 

Current. — The Ampere (formerly called the "weber"), 
= 10-1 absolute units ; practically represented by the 
current which deposits silver at the rate of 0001118 
gramme per second (see Apj)endix B) . 

Electromotive-force. — The Volt, = 10^ absolute units, is that 
E.M.F. which applied to 1 ohm will produce in it a 
current of 1 ampere ; being ifsl of the E.M.F. of a 
Clark standard cell at 15^ C. (See Appendix C.) 

Quantity. — The Coulomb, = lO-i absolute units of quantity ; 
being the quantity of electricity conveyed by 1 ampere 
in one second. 

Capacity. — The Farad, = 10-9 (or one one-thousand- 
millionth) of absolute unit of capacity ; being the capa- 
city of a condenser such as to be changed to a potential 
of 1 volt by 1 coulomb. The microfarad or millionth 
part of 1 farad = lO-i^ absolute units. 

Work. — The Joule, = lO*" absolute units of work (ergs), is 
represented by energy expended in one second by 1 
ampere in 1 ohm. 

Power. — The Watt, = 10 absolute units of power (ergs per 
second), is power of a current of 1 ampere flowing 

* The word " unit " expresses our conception in the abstract of a unit 
quantity, such as those defined in the preceding Articles. A " standard " 
is the concrete thing with wllich we compare quantities to be measured, 
such as a centimetre scale or a standard cell. 



PRACTICAL UNITS 347 



under a pressure of 1 volt. It is equal to 1 joule per 
second, and is approximately rh of one horse-power. 
Induction. — The Henry, = 10'^ absolute units of induction, 
is the induction in a circuit when the electromotire- 
. force induced in this circuit is 1 volt, while the induc- 
ing current varies at the rate of 1 ampere per second. 
Seeing, however, that quantities a million times as great as 
some of these, and a million times as small as some, have to be 
measured by electricians, the prefixes mega- and micro- are 
sometimes used to signify respectively " one million " and " one- 
millionth part." Thus a megohm is a resistance of one million 
ohms, a microfarad a capacity of losSuoo of a farad, etc. The 
prefix kilo- is used for "one thousand," and milli- for "one- 
thousandth part"; thus a kilowatt is 1000 watts, and milli- 
ampere is the thousandth part of 1 ampere. 

The "practical" system may be regarded as a system of 
units derived not from the fundamental units of centimetre, 
gramme, and second, but from a system in which, while the 
unit of time remains the second, the units of length and mass 
are respectively the earth-quadraut and lO-ii gramme. 

355. Use of Index Notation. — Seeing that electricians have 
to deal with quantities requiring in some cases very large num- 
bers, and in other cases very small numbers, to express them, a 
system of index notation is adopted, in order to obviate the use 
of long rows of ciphers. In this system the significant figures 
only of a quantity are put down, the ciphers at the end, or (in 
the case of a long decimal) at the beginning, being indicated by 
an index written above. Accordingly, we may write a thou- 
sand (= 10 X 10 X 10) as 10-3, and the quantity 42,000 may be 
written 42 X 10^. The British National Debt of £770,000,000 
may be written £77 X 10". Fractional quantities will have 
negative indices when written as exponents. Thus tJo (= 0-01) 
= 1 ^ 10 -- 10 = 10-2. And so the decimal 0-00028 will be 
written 28 X lO-s (being = 28 X -OCOOl) . The convenience of this 
method will be seen by an example or two on electricity. The 
electrostatic capacity of the earth is 630,000,000 times that of a 
sphere of one centimetre radius, = 63 X 10' (electrostatic) units. 
The resistance of selenium is about 40,000,000,000, or 4 X lOio 
times as great as that of copper ; that of air is about lO"^^^ qx 

100,000,000,000,000,000,000,000,000 

times as great. The velocity of light is about 30,000,000,000 
centimetres per second, or 3 x lO^o. 

356. Dimensions of Magnetic and Electromagnetic Units. 



348 



ELECTEICITY AND MAGNETISM part ii 



— The fundamental idea of '■ dimensions " is explained in Art. 
284. A little consideration will enable the student to deduce for 
himself the folloTvinsr table : — 





U.xxs. 


DiMEXSIOXS. 




{Magnetic.) 






m 


^ Strength of pole 

' Quantity- of magnetism 




MUiT-^ 


-=v'xorce X (distance)^ = 


\ 


Magnetic potential 


= work -^ strength of pole = 


MlLiT-^ 


H 


Intensity of field 


= force -=- strength of pole = 


mU-*t-^ 


N 


Magnetic Flux 


= intensity x area = 


MUiT-' 


Z 


Reluctance 

(Electromagnetic.) 


= flux -^ mag. potential = 


L 


c 


Current (strength) 


= intensity of field x length = 


Mi Li T"^ 


Q 


Quantity 


= current x time = 


MiL* 


Y 
E 


Potential ) 
Electromotive-force ' 


= work -=- quantity = 


Mi l3. T-- 


E 


Eesistance 


= E.M.F.^ current 


LT-^ 


K 


Capacity 


= quantity -=- potential = 


L-^^T^ 


W 


Power 


= current x potential = 


ML^ T-^^ 


L 
M 


Self-induction ; 
Mutual induction ) 


= E.M.F.-^ current per sec.= 


L 



357. Resistance expressed as a Velocity. — It will be seen, 
on reference to the above table of "Dimensions " of electromag- 
netic units, that the dimensions of resistance are given as LT— i, 
which are the same dimensions (see Art. 284) as those of a velo- 
city. Every resistance is capable of being expressed as a velocity. 
The following considerations may assist the student in forming 
a physical conception of this. Suppose we have a circuit com- 
posed of two horizontal rails (Fig. 176), CS and DT, 1 centim. 
apart, joined at CD, and completed by means of a sliding piece 
AB. Let this variable circuit be placed in a uniform magnetic 
field of unit intensity, the lines of force being directed vertically 
downwards through the circuit. If, now, the slider be moved along 
towards ST with a velocity of n centimetres per second , the number 



EVALUATION OF THE OHM 



349 



of additional lines of force embraced by the circuit will increase at 
the rate n per second ; or, in other words, there will be an induced 
electromotive-force (Art. 225) impressed upon the circuit, which 
will cause a current to flow through the slider from A to B. Let 
the rails have no resistance, then the strength of the current will 
depend on the resistance of AB. Now let AB move at such a 




Q ZA. T 

Fig. 176. 
rate that the current shall be of unit strength. If its resistance 
be one "absolute" (electromagnetic) unit it need only move at 
the rate of 1 centim. per second. If its resistance be greater it 
must move with a proportionately greater velocity ; the velocity 
at which it must move to keep up a current of unit strength being 
numerically equal to its resistance. The resistance known as 
" one ohm " is intended to he lO^ absolute electromagnetic units, 
and therefore is ^represented by a velocity of 10^ centimetres, or 
ten million metres (one earth-quadrant) per second. 

358. Evaluation of the Ohm. — The system of "practical" 
units was originally devised by a committee of the British Asso- 
ciation, who also determined the value of the " ohm " by experi- 
ment in 1863, and constructed standard resistance coils of 
german-silver, called " B.A. Units " or " ohms." 

There are several ways of measuring the absolute value df the 
resistance of a wire. One method (Joule's) is to measure the heat 
produced in it by a known current and calculate its resistance by 
Joule's law (Art. 427). Another method (Weber's) is to measure 
in absolute units the current that is sent through the wire by an 
electromotive-force which is also measured in some absolute way. 
The ratio of the latter to the former gives the value of the-resist- 
ance. Weber's method involved spinning a coil in a magnetic 
field which would generate alternate currents. Kohlrausch used 
an induction coil to generate the E.M.F. Lorenz proposed a 
method in which a disk was spun. Foster a zero method in which 
the E.M.F. in the spinning coil was balanced. Lord Kelvin pro- 
posed to the British Association Committee a modification of 
Weber's method as follows. It being impracticable to give to 
a horizontal sliding-piece so high a velocity as was necessitated, 
the velocity which corresponded to the resistance of a Avire was 
measured in the following way : — a ring of wire (of many turns) , 



I 



350 



ELECTRICITY AND MAGNETISM part ii 



S- 



"— N 



pivoted about a vertical axis, as in Fig. 177, was made to rotate 
very rapidly and uniformly. Such a ring in rotating cuts the lines 
of force of the earth's magnetism. The northern half of the ring, 
in moving from west toward east, will have (see Rule, Art. 225) an 
upward current induced in it, while the southern half, in crossing 
from east toward west, will have a downward current induced in 
it. Hence the rotating ring will, as it spins, act as its own galva- 
nometer if a small magnet he hung at its middle ; the magnetic 
effect due to the rotating coil being proportional directly to the 
horizontal component of the earth's magnetism, to the velocity of 

rotation, and to the number 
of turns of wire in the coil, 
and inversely proportional to 
the resistance of the wire of 
the coils. Hence, all the other 
data being known , the resist- 
ance can be calculated and 
mesiSUYed as a velocity. The 
earliest oluns or B.A. units 
were constructed by compar- 
ison with this rotating coil ; 
but there being some doubt 
as to whether the B.A. unit 
really represented 10^ cen- 
tims. per second, a redeter- 
mination of the ohm was 
suggested in 1880 by the British Association Committee. At the 
firsttnternatioual Congress of Electricians in Paris 1881, the pro- 
ject for a redetermination of the ohm was endorsed, and it was 
also agreed that the practical standards should no longer be con- 
structed in German silver wire, but that they should be made 
upon the plan originally suggested by Siemens, by defining the 
practical ohm as the resistance of a column of pure mercury of a 
certain length, and of one millimetre of cross-section. The orig- 
inal "Siemens' unit" was a column of mercury one metre in 
length, and one square millimetre in section, and was rather less 
than an ohm (O'SkllO B.A. unit) . Acting on measurements made 
by leading physicists of Europe, the Paris Congress of 1884 de- 
cided that the mercury column representing the '^ legal" ohm 
should be 106 centimetres in length. This was, however, never 
legalized in this country or in America, as it was known to be 
incorrect. Lord Rayleigh's determination gave lOG-21 centi- 
metres of mercury, as representing the true theoretical ohm ( = 
10-* absolute units) : and Rowland's determinatious at Baltimore 




^ 



Fig. 1' 



RATIO OF UNITS 



351 



came slightly higher. The British Association Committee in 1892 
agreed to lengthen it to 106"3 centims., and to define by mass 
instead of section. This was decided finally as the international 
ohm by the Congress of Chicago in 1893. These international 
units are now legalized in England and the United States. The 
bulletin issued by the U. S. Superintendent of Standard Weights 
and Measures, and endorsed by the Secretary of the U. S. Treas- 
ury, is given in abstract in Appendix B. 

The old B.A. unit is only 0"9863 of the true ohm; the Sie- 
mens" unit is only 0'9108. 

359. Ratio of the Electrostatic to the Electromagnetic 
Units. — If the student will compare the Table of Dimensions of 
Electrostatic Units of Art. 283 with that of the Dimensions of 
Electromagnetic Units of Art. 356, he will observe that the dimen- 
sions assigned to similar units are different in the two systems. 
Thus, the dimensions of "Quantity" in electrostatic measure 
are M^ L^ T~ , and in electromagnetic measure they are M^ L-- 
Dividing the former by the latter we get LT~ ' a quantity which 
we at once see is of the nature of a velocity. This velocity occurs 
in every case in the ratio of the electrostatic to the electromag- 
netic measure of every unit. It is a definite concrete velocity, 
and represents that velocity at which 'two electrified particles 
must travel along side by side in order that their mutual electro- 
magnetic attraction (considered as equivalent in so moving (Art. 
397) to two parallel currents) shall just equal their mutual elec- 
trostatic repulsion (see Art. 260). This velocity, " v," which is 
of enormous importance in the electromagnetic theory of light 
(Art. 518), has been measured in several ways. 



Unit. 


Electrostatic. 


Electromag>'etic. 


Ratio. 


Quantity . 
Potential . 
Capacity . 
Resistance . 


M^Li T-^ 

mH* t-^ 

L 

L 1 T 


m*l4 

M^ Li T-' 
L-^T^ 
L T-^ 


LT-^ =v 

L-^T=l/v 
L2 T-^= V^ 

l-'t'^=iA2 



(a) Weber and Kohlrausch measured the electrostatic unit of 
quantity and compared it with the electromagnetic unit of quan- 
tity, and found the ratio v to be=3-1074X IQi'' centims. per second., 



352 ELECTRICITY AND MAGNETISM part ii 

(6) Lord Kelvin compared the two units of potential and 
found 

V = 2-825 X 1010, 
and later, = 2-93 x lOW. 

(c) Professor Clerk Maxwell balanced a force of electrostatic 
attraction against one of electromagnetic repulsion, and found 

V = 2-88 X 1010. 

(d) Professors Ayrtou and Perry measured the capacity of a 
condenser electromagnetically by discharging it into a ballistic 
galvanometer, and electrostatically by calculations from its size, 
and found 

V = 2-980 X 1010. 

The velocity of light according to latest values is — 
= 2-9992 X 1010; 
so we take r as 3 x IQio, or thirty thousand million centimetres 
per second. 

360. Rationalization of Dimensions of Units. — It seems ab- 
surd that there should be two different units of electricity ; still 
more absurd that one unit should be thirty thousand million centi- 
metres per second greater than the other. It also seems absurd 
that the dimensions of a unit of electricity should have fractional 
powers, since such quantities as M- and L"2 are meaningless. 
These irrational things arise from the neglect to take account of 
the properties of the medium in applying the law of inverse 
squares to form definitions of the unit of electricity in the 
electrostatic system, and of the unit-pole in the magnetic system. 
If we were to insert the dielectric constant k in the former, and the 
permeability m in the latter, we might, if we knew the dimensions 
of these quantities, be able to rationalize the dimensional formu- 
la. But we do not know their dimensions. Rticker has, however, 
shown that they can be rationalized, and the two sets of units 
brought into agreement,* by assuming that the product ^•/x has 
the dimensions of the reciprocal of the square of a velocitj' : or 
c = l/sT/j/x. If k were the reciprocal of the rigidity of the ether, 
and M its density, r would represent the velocity of propagation of 
waves in it. Compare Art. 518 on electromagnetic theory of light. 

361. Earth's Magnetic Force in Absolute Units. — In mak- 
ing absolute determinations of current by the tangent galva- 
nometer, or of electromotive-force by the spinning coil, it is need- 
ful to know the absolute value of the earth's magnetic field, or 
of its horizontal component. The intensity of the earth's mag- 
netic force at any place is the force -with which a magnet-pole of 

* See Everett's Units and Physical Constants, 4th edition (1S93), p. '21)3. 



MAGNETIC MEASUREMENTS 353 



unit strength is attracted. As explained in Art. 153, it is usual 
to measure the horizontal component H of this force, and from 
this and the cosine of the angle of dip to calculate the total 
force, as the direct determination of the latter is surrounded with 
difficulties. To determine H in absolute (or C.G.S.) units, it is 
necessary to make two observations with a magnet of magnetic 
moment M (Art. 135). In one of these observations the product 
iSIH is determined by a method of oscillations (Art. 133) ; in the 

second the quotient ^ is determined by a particular method of 

H 
deflexion (Art. 138). The square root of the quantity obtained 
by dividing the former by the latter will, of course, give H. 

(i.) Determination of ]MH. — The time T of a complete 
oscillation to and fro of a magnetic bar is 

T = 2 -a/^, 

\mh 

where K is the "moment of inertia" of the magnet. This for- 
mula is, however, only true for very small arcs of vibration. 
By simple algebra it follows that 

MH=:i^. 

T2 

Of these quantities T is ascertained by a direct observation 
of the time of oscillation of the magnet hung by a torsionless 
fibre ; and K can be either determined experimentally or by 
one of the following formulae : — 

For a round bar K = io(— + — 

Vl2 4 

For a rectangular bar K = to ( " *" " | ; 

where to is the mass of the bar in grammes, I its length, a its 
radius (if round), 6 its breadth, measured horizontally (if rec- 
tangular) . 

M 
(ii.) Determination of — . — The magnet is next caused to 
H 
deflect a small magnetic needle in the following manner," broad- 
side on." The magnet is laid horizontally at right angles to the 
magnetic meridian, and so that its middle point is (magnetically) 
due south or due north of the small needle, and at a distance r 
from its centre. Lying thus broadside to the small needle its 
N pole will repel, and its S pole attract, the N pole of the needle, 
and will exercise contrary actions on the S pole of the needle. 
The total action of the magnet upon the needle will be to deflect 
the latter through an angle 5, whose tangent is directly propor- 
2a 



354 ELECTRICITY AND MAGNETISiVI part ii 



M 
tional to — , and inversely proportional to the cube of the dis- 

tance y'; or — ^r^tanS. 

H 
Dividing the former equation by this, and taking the square 
root, we get 

T V " 



v^ tan 

Lesson XXVIII. — Properties of Iron and Steel 

362. Magnetization of Iron. — When a piece of mag- 
netizable metal is placed in a magnetic field, some of the 
lines of magnetic force run through it and magnetize it. 
The intensity of its magnetization will depend upon the 
intensity of the field into which it is put and upon the 
metal itself. There are two ways of looking at the matter, 
each of which has its advantages. We may think about 
the internal condition of the piece of metal, and of the 
number of magnetic lines that are running through it 
and emerging from it into the surrounding space. This 
is the modern way. Or we may think of the magnetism 
of the iron or other metal as something resident on the 
polar surfaces, and expressed therefore in units of mag- 
netism. This is the old way. The fact that soft iron 
placed in the magnetic field becomes highly magnetic may 
then be expressed in the following two ways : (1) when 
iron is placed in the magnetic field, the magnetic lines run 
in greater quantities through the space now occupied by 
iron, for iron is very permeable to the lines of magnetic 
induction, being a good conductor of the magnetic lines ; 
(2) iron when placed in the magnetic field develops 
strong poles on its end-surfaces, being highly susceptible 
to magnetization. Each of these ideas may be rendered 
exact by the introduction of appropriate coefficients. 

363. Permeability. — The precise notion now at- 
tached to this word is that of a numerical coefficient. 
Suppose a magnetic force — due, let us say, to the circula- 
tion of an electric current in a surrounding coil — were to 



PEEMEABILITY 355 



act on a space occupied by air, there would result a certain 
number of magnetic lines in that space. In fact, the 
intensity of the magnetic force, symbolized by the letter 
H, is often expressed by saying that it would produce H 
magnetic lines per square centimetre in air. I^ow, owing 
to the superior magnetic power of iron, if the space 
subjected to this magnetic force were filled with iron 
instead of air, there would be produced a larger number 
of magnetic lines per square centimetre. This larger 
number of magnetic lines in the iron expresses the 
degree of magnetization * in the iron ; it is symbolized 
by the letter B. The ratio of B to H expresses the 
permeahility of the material. The usual symbol for per- 
meability is the Greek letter /x. So we may say that B 
is equal to fx times H, or 

IX = B/H. 

For example, a certain specimen of iron, when sub- 
jected to a magnetic force capable of creating, in air, 50 
magnetic lines to the square centimetre, was found to be 
permeated by no fewer than 16,062 magnetic lines per 
square centimetre. Dividing the latter figure by the 
former gives as the value of the permeability at this 
stage of the magnetization 321, or the permeability of 
the iron is 321 times that of air. 

The permeability is always positive : for empty space 
it is 1, for air it is practically 1 ; for magnetic materials 
it is greater than 1, for diamagnetic materials it is slightly 
less than 1. In air, etc., B = H. 

Where the magnetic lines emerge into the air at a 
polar surface they are of course continuous with the 
internal lines : the value of B just inside the polar sur- 
face is the same as that of B in the air just outside it. 

The permeability of such non-magnetic materials as 

* The actual number of magnetic lines that run through unit area of 
cross-section in the iron or other material — denoted by the symbol B — is 
called by several names — " the permeation," " the internal magnetization," 
or "the induction." The last name, unfortunately used by Maxwell and 
Hopkinson, is to be avoided. A better name is " flux density." 



356 ELECTRICITY AND MAGNETISM part ii 

silk, cotton, and other insulators, also of brass, copper, 
and all the non-magnetic metals, is taken at 1, being 
practically the same as that of the air. 

This mode of expressing the facts is, however, com- 
plicated by the fact of the tendency in all kinds of iron 
to magnetic saturation. In all kinds of iron the mag- 
netizability of the material becomes diminished as the 
actual magnetization is pushed further. In other words, 
when a piece of iron has been magnetized up to a certain 
degree, it becomes, from that degree onward, less perme- 
able to further magnetization, and though actual satura- 
tion is never reached, there is a practical limit beyond 
which it cannot well be pushed. Joule discovered this 
tendency to a limit. The practical limit of B in good 
wrought iron is about 20,000 lines per square centimetre, 
or in cast iron about 12,000. Using extraordinary mag- 
netizing forces, Ewing has found it possible to increase 
B to 45,000, and Du Bois has reached 60,000 lines per 
square centimetre. Manganese steel is curiously non- 
magnetic : Hopkinson found 310 as the maximum B. 

364. Curves of Magnetization. — A convenient mode 
of studying the magnetic facts respecting any particular 

brand of iron is to plot on a 
160001 '-oFi^jjiili^lll^^"'"; ~' diagram the curve of mag- 
netization — i.e. the curve in 
which the values, plotted 
horizontally, represent the 
magnetic force H, and the 
values plotted vertically those 
that correspond to the respec- 
tive magnetization B. In Fig. 
^°' ' ■ 178, which is modified from 

the researches of Ewing, are given five curves relating 
to soft iron, hardened iron, annealed steel, hard-drawn 
steel, and glass-hard steel. It will be noticed that all 
these curves have the same general form, and that there 
are three stages. (1) For small values of H the values of 




CURVES OF MAGNETIZATION 



357 



B are small, and as H is increased B increases gradually. 
(2) The curve rises very suddenly, at least with all the 
softer sorts of iron. (3) The curve then bends over and 
becomes nearly horizontal, B increasing very slowly. 
AThen the magnetization is in the stage below the bend 
of the curve, the iron is said to be far from the state of 
saturation. But when the magnetization has been pushed 
beyond the bend of the curve into the third stage, the 
iron is said to be approaching saturation, because at this 
stage of magnetization it requires a large increase in the 
magnetizing force to produce even a very small increase 
in the magnetization. It will be noted that for soft 
wrought ii'ou the stage of approaching saturation sets in 
when B has attained the value of about 16,000, or when 
H has been raised to about 50. The student is strongly 
advised to plot for himself similar curves from the sub- 
joined table, which relates to the permeabilities of some 
samples of u'on examined by Hopkinson. 



Anxealee 


Weottght Irox. 


Gre\ 


Cast Iron. 


B 


^ 


H 


B 


/«■ 


H 


5,000 


3000 


1-66 


4,000 


800 


5 


9,000 


2250 


4 


5,000 


500 


10 


10,000 


2000 


5 


6,000 


279 


21-5 


11,000 


1692 


6-5 


7,000 


133 


42 


12,000 


1412 


8-5 


8,000 


100 


80 


13,000 


1083 


12 


9,000 


71 


127 


14,000 


823 


17 


10,000 


53 


188 


15,000 


526 


28-5 


11,000 


37 


292 


16,000 


320 


50 








17,000 


161 


105 








18,000 


90 


200 








19.000 


54 


350 








20,000 


30 


666 









It will be noted that at early stages of the magnetiza- 



358 ELECTRICITY AND MAGNETISM part ii 

tion, in moderately weak fields where H is less than 
about 5, the permeability has enormous values. But 
for values of H less than about 0*5 the permeability is 
quite small, usually about 300. 

The three stages observed in the magnetization are 
explained in Swing's molecular theory (Art. 127). 

If iron is compressed its permeability decreases ; if 
subjected to tensile stress it is increased, provided the 
field is not too intense. Yillari found that beyond a cer- 
tain intensity tension diminishes the permeability. 

365. Susceptibility. — Suppose a magnet to have 
m units of magnetism on each pole ; then if the length 
between its poles is Z, the product ml is called its magnetic 
moment, and the magnetic moment divided by its volume 
is called its intensity of magnetization ; this term being 
intended, though based on surface-unit of pole strength, 
to convey an idea as to the internal magnetic state. 
Seeing that volume is the product of sectional area into 
length, it follows that if any piece of iron or steel of 
uniform section had its surface magnetism situated on its 
ends onl}^, its intensity of magnetization would be equal 
to the strength of pole divided by the area of end-sui-f ace. 
Writing I for the intensity of magnetization we should 
have 

J _ mag, moment _ m X I _ m _ 
volume s X I s 

N"ow, supposing this intensity of magnetization were 
due to the kon having been put into a magnetic field of 
intensity H, the ratio between the resulting intensity of 
magnetization I and the magnetizing force H producing 
it is expressible by a numerical coefficient of magnetiza- 
tion, or susceptibility, k. We may write 

I = AH, 
or k = I/H. 

This may be looked at as saying that for every 



LIMIT OF MAGNETIZATION 



359 



magnetic line in the field there will be k units of 
magnetism on the end-surface. In magnetic substances 
such as iron, steel, nickel, etc., the susceptibility k has 
positive values ; but there are many substances such as 
bismuth, copper, mercury, etc., which possess feeble 
negative coefficients. These latter are termed " diamag- 
netic " bodies (Art. 369) and are apparently repelled by 
the poles of magnets. It was shown at end of Art. 338 
that there are Itt magnetic lines proceeding from each 
unit of pole magnetism. Hence if, as shown above, each 
line of force of the magnetizing field produces k units of 
magnetism there will be 47^^' lines added by the iron to 
each 1 line in the field, or the permeability of the iron 
fjL is equal to 1 + 47^^^ It follows that B = H + 4:7rkB.. 
This shows that B may go on increasing as long as H 
is increased, having no true limit. But since k decreases 
as saturation sets in, the surface magnetization I (or B — H 
to which it is proportional) may have a true limit. This 
maximum of B — H appears to be about 21,360 in 
wrought iron, 15,580 in cast iron, and 5660 in nickel. 

In the following table are given some figures from 
the researches of Bidwell on wrought iron. 



H 


Jc 


I 


/«• 


B 


3-9 


151-0 


587 


1899-1 


7390 


10-3 


89-1 


918 


1121-4 


11550 


40- 


30-7 


1226 


386-4 


15460 


115- 


11-9 


1370 


150-7 


17330 


208- 


70 


1452 


88-8 


18470 


427- 


3-5 


1504 


45-3 


19330 


585- 


2-6 


1530 


33-9 


19820 



Everett has calculated (from Gauss's observations) 
that the intensity of magnetization of the earth is only 
0-0790, or only j^o of what it would be if the globe 



360 ELECTRICITY AXD MAGNETISM part ii 

were wholly iron. In weak magnetic fields the suscep- 
tibility of nickel exceeds by about five times that of iron ; 
but m strong fields iron is more susceptible. 

366. Measurement of Permeability. — There are 
several ways of measuring the permeabilit}^ of iron : they 
aU involve a measurement of B. 

(a) Magnetometer Methods. — The pole strength of long 
bars, when magnetized by a coil around them, can be 
measm-ed by a magnetometer (Art. 138), and from this 
N is found by multiplying by ^tt. 

(6) Induction Methods. — Rings of iron which, having 
no poles, cannot be measured by the magnetometer are 
measured inductively. Upon the ring is wound a mag- 
netizing coil, and also an exploring coil (Art. 232) which 
is connected to a ballistic galvanometer. On turning on 
or off the magnetizing current, or reversing it, induced 
currents are generated, giving a throw in the galva- 
nometer proportional to the number of magnetic lines 
which have been made or destroyed. Iron rods can be 
examined by the same means. 

(c) Traction Methods. — The pull needed to separate 
the two halves of a divided rod, or divided ring, is (Art. 
884) proportional to the square of B. Bidwell and others 
have used this for measuring permeability. 

(c?) Optical Methods. — Du Bois has used a method 
based on Kerr's discovery (Art. 527) of magneto-optic 
rotation. 

367. Residual Effects. — The retention of mag- 
netism by steel, lodestone, hard iron, and even by soft 
iron if of elongated shape, has been akeady described 
(Art. 98). Some other residual effects must now be 
noted. It is found that if a new piece of iron or steel is 
subjected to an increasing magnetizing force, and then the 
magnetizing force is decreased to zero, some magnetism 
remains. If the results are plotted out in a curve it 
exhibits the foUoNving peculiarities. On first gTaduaUy 
increasing H from o, B rises as we have seen in Art. 364. 



CHAP. T 



CYCLES OF MAGNETIZATION 



361 




If when the curve has risen to a (Fig. 179) H is now 
decreased, the descending curve does not follow the 
ascending curve, owing to the retention of the magne- 
tism. When H has been reduced to zero the point h is 
reached. This the residual value 
of B is called the remanence, and 
depends on the material, and on 
the degree to which B was pre- 
viously pushed. If now a re- 
versed magnetizing force — H is 
now applied it is found that it 
must be increased to a definite 
degree in order to demagnetize 
the iron and bring the curve down 
to c. The amount of reversed 
magnetic force so needed is a 
measure of the retentivity of the 
material, and is known as the 
coercive force. In hard steel it may amount to 100 ; in 
soft steel to 20 ; in soft iron to 2 or less. If the reversed 
magnetizing force is further increased, the curve descends 
from c to d, the iron becoming magnetized with reversed 
polarity, and going toward saturation. On then dimin- 
ishing the reversed force to zero, the curve turns to e, 
showing a negative remanence. On again increasing H 
as at first the curve ascends to /, and as the former value 
of H is reached comes up to a again. 

368. Cycles of Magnetization. Hysteresis. — When 
H is thus carried through a cycle of increase and 
decrease, B also goes through a cycle ; and as we have 
seen there is a lagging in the magnetization, evidenced in 
Fig. 179 by the formation of a closed loop in the curve. 
Warburg and Ewing, who have fully investigated the 
phenomenon, have remarked that the area enclosed 
indicates the waste of energy in the cycle of operations. 
In hard steel the areas of these loops are much wider 
than in the case of soft iron. Ewing has given the name 



362 



ELECTKICITY AST) MAGNETISM part ii 



of Hysteresis to the subject of the lag of magnetic effects 
behind their causes. From his researches* also is taken 
the case of Fig. 180. a specimen of soft iron, the curve 
for which shows various loops. Ewing has devised a 
curve-tracer for recording the curves automatically. The 

waste of energy per cubic 
centimetre in a cycle of 
strong magnetization may 
vary from 9000 ergs in 
annealed iron to 200,000 
in glass-hard steel. If (as 
in the iron cores of alter- 
nate current transformers) 
the cycle is repeated 100 
t"- times a second the waste 
of power by hysteresis may 
heat the iron; and it in- 
creases greatly with the 
frequency and with the 
degree to which the mag- 
netization is pushed. If B 
does not exceed 5000, the 
power wasted at 100 cycles 
per second in every cubic 
foot of iron may be as low 
as 57.5 watts, but if B is increased to 10,000 the waste 
becomes 1560 watts. 

Since a smaller reversed force suffices to destroy mag- 
netization than was required to produce it, all that is 
necessaiy in order to completely demagnetize iron is to 
subject it to a series of cycles of diminishing intensity. 

Mechanical agitation tends to help the magnetizing 
forces to act, and lessens all residual and hysteresial 
effects. 

Ewing has also shown that under constant magnetizing 

* The stndent should not fail to consult Ewing's book. Magnetic In- 
duction in Iron. 




DI A MAGNETISM 



363 



force the magnetism will go on slowly and slightly in- 
creasing for a long time : this is called magnetic creep- 
ing, or viscous hysteresis. 



Lessox XXIX. — Diamagnetisrh ' 



In 1778 Brugmans 



369. Diamagnetic Experiments. 

of Leyden observed that when a lump of bismuth was 
held near either pole of a magnet needle it repelled 
it. In 1827 Le Baillif and Becquerel observed that the 
metal antimony also could repel and be repelled by the 
pole of a magnet. In 181:5 Faraday, using powerful 
electromagnets, examined the magnetic properties of a 
large number of substances, and found that whilst a 
great many are, like iron, attracted to a magnet, others 
are feebly repelled. To distinguish between these two 
classes of bodies, he termed those which are attracted 
paramagnetic,* and those which are repelled diamagnetic. 
The property of being thus apparently repelled from a 
magnet he termed diamagnetism. 

Faraday's method of experiment consisted in suspend- 
ing a small bar of the substance in 
a powerful magnetic field between 
the two poles of an electromagnet, 
and observing whether the small 
bar was attracted into an axial 
position, as in Fig. 181, with its 
length along the line joining the 
two poles, or whether it was re- 
pelled into an equatorial position, 
at right angles to the line joining 
the poles, across the lines of force 
of the field, as is shown by the position of the small bar 
in Fig. 182, suspended between the poles of an electro- 
magnet constructed on Ruhmkorff' s pattern. 

* Or simply "magnetic." Some authorities use the term "ferro- 
magnetic." 




Fig. 181. 



364 ELECTRICITY AND MAGNETISM part ir 



I 



I 




Fig. lS:i. 

370. Results. — The following are the principal sub- 
stances examined by the method : — 



* 



Paramagnetic. 


Dl.VJIAGNETIC. 


Iron 


Bismuth 


Nickel 


Phosphorus 


Cobalt 


Antimony 


Manganese 


Thallium 


Chromium 


Zinc 


Cerium 


Mercury 


Titanium 


Lead 


Platinum* 


Silver 


Many ores and salts 


Copper 


containing the 


Gold 


above metals 


Water 


Oxygen gas 


Alcohol 


Oxygen liquid 


Tellurium 


Ozone 


Sulphur 



* Chemically pure Platinum is diamagnetic, according to Wiedemann. 



DIAMAGNETISM 365 



Liquids were placed in glass vessels and suspended 
between the poles of the electromagnet. Almost all 
liquids are diamagnetic, except solutions of salts of the 
magnetic metals, some of which are feebly magnetic; but 
blood is diamagnetic though it contains iron. To examine 
gases bubbles are blown with them, and watched as to 
whether they were drawn into or pushed out of the field. 
Oxygen gas was found to be magnetic ; ozone has been 
found to be still more strongly so. Dewar has found 
liquid oxygen sufficiently magnetic to rush in drops to the 
poles of a powerful magnet. 

The diamagnetic properties of substances may be 
numerically expressed in terms of their permeability or 
their susceptibility (Arts. 363 and 365). For diamagnetic 
bodies the permeability is less than unity. For bisn:iuth 
the value of fx is 0-999969. The repulsion of bismuth is 
immensely feebler than the attraction of iron. Pliicker 
estimated the relative magnetic powers of equal weights 
of substances as follows : — 

Iron + 1,000,000 

Lodestone Ore + 402,270 

Ferric Sulphate + 1,110 

Ferrose Sulphate + 780 

Water — 7-8 

Bismuth — 23*6 

371. Apparent Diamagnetism due to surrounding 
Medium. — It is found that feebly magnetic bodies be- 
have as if they were diamagnetic when suspended in a 
more highly magnetic fluid. A small glass tube filled 
with a weak solution of ferric chloride, when suspended 
in air between the poles of an electromagnet, points 
axially, or is paramagnetic ; but if it be surrounded by 
a stronger (and therefore more magnetic) solution of 
the same substance, it points equatorially, and is appar- 
ently repelled like diamagnetic bodies. All that the 
equatorial pointing of a body proves then is, that it is less 
magnetic than the medium that fills the surrounding space. 



866 ELECTRICITY AND MAGNETISM part ii 

A balloon, though it possesses mass and weight, rises 
through the air in obedience to the law of gravity, because 
the medium surrounding it is more attracted than it is. 
But it is found that diamagnetic repulsion takes place even 
in a vacuum : hence it would appear that the ether of 
space itself is more magnetic than the substances classed 
as diamagnetic. 

372. Diamagnetic Polarity. — At one time Faraday 
thought that diamagnetic repulsion could be explained 
on the supposition that there existed a " diamagnetic 
polarity" the reverse of the ordinary magnetic polarity. 
According to this view, which, however, Faraday himself 
quite abandoned, a magnet, when its N pole is presented 
to the end of a bar of bismuth, induces in that end a 
N pole (the reverse of what it would induce in a bar of 
iron or other magnetic metal), and therefore repels it. 
Weber adopted this view, and Tyndall warmly advocated 
it, especially after discovering that the repelling diamag- 
netic force varies as the square of the magnetic power 
employed. It has even been suggested that when a 
diamagnetic bar lies equatorially across a field of force, its 
east and west poles possess different properties. The ex- 
periments named above suggest, however, an explanation 
less difficult to reconcile with the facts. It has been 
pointed out (Art. 363) that the degree to which mag- 
netization goes on in a medium depends upon the magnetic 
permeability of that medium. Kow, permeability ex- 
presses the number of magnetic lines induced in the 
medium for every line of magnetizing force applied. A 
certain magnetizing force applied to a space containing air 
or vacuum would induce a certain number of magnetic 
lines through it. If the space considered were occupied 
by a paramagnetic substance it would concentrate the 
magnetic lines into itself, as the sphere does in Fig. 183. 
But if the sphere were of a permeability less than 1, the 
magnetic lines would tend rather to pass through the air, 
as in Fig. 184. If the space considered were occupied by 



CHAP. V DIAMAGXETIC ACTION 36T 

bismuth, the same magnetizing force would induce in the 
bismuth fewer magnetic lines than in a vacuum. But 
those lines which were induced 
would still run in the same ^ ^ liiiirz:^ ^ 

general direction as in the '- ^ ^7s?^i< ^ 

vacuum; not in the opposite ^ zYz'i-yy?' ^ 

direction, as Weber and Tyndall - ^ ^i-yr'-^^j ^ 

maintained. The result of '^ ^^^^^^^ 

there being a less induction ' "^ 

through diamagnetic sub- Fig. 183. 

tances can be shown to be that such substances will 
be urged from places where the magnetic force is strong 
to places where it is weaker. 
-^ =:: ^ This is why a ball of bismuth 

: :-?^-vv? ^ moves away from a magnet, 

t "- 1 and why a little bar of bismuth 

% v?r::i'-v: ^ between the conical poles of 

^ ^ ^^^^^^ ^ the electromagnet (Fig. 182) 

turns equatorially so as to put 

Fig- 1S4. its ends into the regions that 

are magnetically weaker. There is no reason to doubt 

that in a magnetic field of uniform strength a bar of 

bismuth would point along the lines of induction. 

373. Magne-Crystallic Action. — In 1822 Poisson pre- 
dicted that a body possessing crystalline structure would, 
if magnetic at all, have different magnetic powers in 
different directions. In 18-17 Pliicker discovered that a 
piece of tourmaline, which is itself feebly paramagnetic, 
behaved as a diamagnetic body when so hung that the 
axis of the crystal was horizontal. Faraday, repeating 
the experiment with a crystal of bismuth, found that it 
tended to point with its axis of crystallization along the 
lines of the field axially. The magnetic force acting thus 
upon crystals by virtue of their possessing a certain 
structure he named magne-crystallic force. Pliicker en- 
deavoured to connect the magne-crystallic behaviour of 
crystals with their optical behaviour, giving the following 



368 ELECTRICITY AND MAGNETISM part ii 

law : there will be either repulsion or attraction of the 
optic axis (or, in the case of bi-axial crystals, of hoth optic 
axes) by the poles of a magnet; and if the crystal is a 
"negative" one {i.e. optically negative, having an extra- 
ordinary index of refraction less than its ordinary index) 
there will be repulsion, if a " positive " one there will be 
attraction. Tyndall has endeavoured to show that this 
law is insufficient in not taking into account the para- 
magnetic or dianiagnetic powers of the substance as a 
whole. He finds that the magne-crystallic axis of bodies 
is in general an axis of greatest density, and that if the 
mass itself be paramagnetic this axis will point axially ; if 
diamagnetic, equatorially. In bodies which, like slate and 
many crystals, possess cleavage, the planes of cleavage 
are usually at right angles to the magne-crystallic axis. 
Another way of stating the facts is to say that in non- 
isotropic bodies the induced magnetic lines do not nec- 
essarily run in the same direction as the lines of the 
impressed magnetic field. 

374. Diamagnetism of Flames. — In 1847 Bancalari 
discovered that flames are repelled from the axial line 
joining the poles of an electromagnet. Faraday showed 
that all kinds of flames, as well as ascending streams of 
hot air and of smoke, are acted on by the magnet, and 
tend to move from places where the magnetic forces are 
strong to those where they are weaker. Gases (except 
oxygen and ozone), and hot gases especially, are feebly 
diamagnetic. But the active repulsion and turning aside 
of flames may possibly be in part due to an electromag- 
netic action like that which the magnet exercises on the 
convexion-current of the voltaic arc (Art. 448) and on 
other convexion-currents. The electric properties of 
flame are mentioned in Arts. 8 and 314. 



THE MAGNETIC CIRCUIT 369 



Lesson XXX. — The Magnetic Circuit 

375. Magnetic Circuits. — It is now generally recog- 
nized that there is a magnetic circuit law similar to the 
law of Ohm for ■ electric circuits. Ritchie, Sturgeon, 
Joule, and Faraday dimly recognized it. But the law 
was first put into shape in 1873 by Rowland, who calcu- 
lated the flow of magnetic lines through a bar by dividing 
the '' magnetizing force of the helix " by the " resistance 
to lines of force " of the iron. In 1882 Bosanquet intro- 
duced the term magnetomotive-force, and showed how to 
calculate the reluctances of the separate parts of the mag- 
netic circuit, and, by adding them, to obtain the total 
reluctance.* 

The law of the magnetic circuit may be stated as 
follows : — 

Magnetic Flux = niagnetomotive-force , 
° reluctance 

TVT M 

orN=_. 

376. Reluctance. — As the electric resistance of a 
prismatic conductor can be calculated from its length, 
cross-section, and conductivity, so the magnetic reluctance 
of a bar of iron can be calculated from its length, cross- 
section, and permeability. The principal difference be- 
tween the two cases lies in the circumstance that whilst 
in the electric case the conductivity is the same for small 
and large currents, in the magnetic case the permeability 
is not constant, but is less for large magnetic fluxes than 
for small ones. 

Let the length of the bar be I centiras., its section A 
sq. cms., and its permeability fx. Then its reluctance 

* This useful term, far preferable to "magnetic resistance," was intro- 
duced by Oliver Heaviside. The term reluctivity is sometimes used for 
the specific reluctance ; it is the reciprocal of permeability. 
2b 



370 



ELECTRICITY AXD MAGNETIS.M part ii 



will be proportional directly to /, and inversely to A and 
fx. Calling the reluctance Z we have 

Z = Z/A/x. 

Example. — An iron bar 100 cm. long and 4 sq. cms. in 
cross-section is magnetized to such a degree that ix = 320: 
then Z will be 0-078. 

The reluctance of a magnetic circuit is generally made 
up of a number of reluctances in series. We will first 
take the case of a closed magnetic circuit (^ig. 185) made 
up of a curved iron core of length /^ section Aj, and 
permeability /x^ ; and an armature of 
length 1.2, section A2, and permeability /Xg* 
in contact with the ends of the former. 
In this case the reluctance is 




Aj/xj A2/X2 

377- Calculation of Exciting Power.' — 
Passing on to the more difficult case of 
a circuit made up partly of ii'on and partly of air, we 
will suppose the armature to be moved to a distance? 
so that there are two air-gaps in the circuit, each gap 
of length Zo (from iron to iron), and sec- 
tion A3 (equal to area of pole face). 
This will introduce an additional reluc- 
tance 2Z3/A3, the permeability for air 
being = 1. It wiU also have the effect of 
making part of the magnetic flux leak 
out of the circuit. 

By Art. 341, if the exciting power 
consists of C amperes circulating in S 
spirals around the core, the magneto- 
motive-force wdll be -iTrCS/lO. Applying 
this to the preceding example, dividing the magneto- 
motive-force by the reluctance, we get for the magnetic 
flux — 




Fig. 1S6. 



CHAP. V CALCULATION OF EXCITATION 371 



IrrCS 



But more often the calculation is wanted the other 
way round, to find how many ampere-turns of excitation 
will be needed to produce a given flux through a magnetic 
circuit of given size. Two difficulties arise here. The 
permeability will depend on the degree of saturation. 
Also the leakage introduces an error. To meet the first 
difficulty approximate values of jx must be found. Sup- 
pose, for example, it was intended to produce a flux of 
1,000,000 lines through an iron bar having a section of 
80 sq. centims., then B will be 12,500, and reference to 
the table in Art. 364 shows that if the bar is of wrought 
ii'on fjL will be about 1247. To meet the second difficulty 
we must estimate (from experience) an allowance for 
leakage. Suppose we find that of all the lines created in 
the U-shaped part only the fraction 1/v gets through 
the armature, then to force N lines through the armature 
we must generate v'N lines in the U-shaped piece, where 
V is the coefficient of allowance for leakage, an improper 
fraction increasing with the width of the gaps. 

We then proceed to calculate in parts as follows : — 

Ampere-turns needed to drive N lines 1 _ jr w h ^i-257 
through iron of armature. J -^ii^i 

Ampere-turns needed to drive N lines | ^ jr ^ ^ ^ 1-257 
through two gaps. I A3 ' " 

Ampere-turns needed to drive I'N lines I _ j,™- x ^2 ^ 1-957 
through iron of magnet core. J A21U2 

Then adding up, we get : — 

Total ampere-turns needed = N \ -^ — 1"-:^ + ^ f - 1*257. 

( Ai^i A2U2 A3 J 

Formulse similar to this have been used by Hopkinson 
and by Kapp in designing electromagnets for dynamos. 
378. Effect of Air-Gap in Circuit. — Air having no 



372 ELECTEICITY AND MAGNETISM part ii 

remanence the presence of a gap in the iron circuit tends 
to make residual magnetism unstable, as though the 
polar magnetism on the end-faces had a self-demagnetiz- 
ing effect. In fact it is very difficult to give a permanent 
magnetism to short pieces of metal. Further, the low 
permeability of air necessitates enormous magnetomotive- 
forces, compared with those required for iron, to produce 
a given flux. The effect is to shear over to the right the 
curves of magnetization, seeing that a greater H is needed 
to attain an equal value of B. Joints in the magnetic 
circuit have the same kind of effect. 

The reason why the pull exerted by an electromagnet 
on its armature falls off so very greatly when the arma- 
ture is moved away to a short distance is the diminution 
of the magnetic flux caused by the great reluctance of 
the air-gap thus introduced into the circuit. 

379. General Law of Electromagnetic Systems. — 
Consider an electromagnetic system consisting of any 
number of parts — iron masses, coils carrying currents, 
air, masses of other materials, whether magnetic or 
diamagnetic — in any given configuration. Any change 
in the configuration of the parts will in general produce 
either an increase or a decrease in the magnetic flux. For 
example, if the armature of an electromagnet is allowed 
to move up toward the poles, or the needle of a galvano- 
meter is allowed to turn, there will be a betterment of 
the magnetic circuit, and the magnetic flux through the 
coils will be increased. Magnetic circuits always tend to 
close up and become as compact as possible. On the con- 
trary, if we pull away the armature from an electromag- 
net the magnetic reluctance is increased, and the flux 
diminished ; and this action is resisted by the reaction of 
the system. All these things may be summed up in the 
following general law : — 

Every electromagnetic system tends so to chaiige the con- 
figuration of its parts as to make the magnetic flux a 
maximum. 



CHAP. T LAW OF ELECTROMAGNET 373 

Suppose (the exterual magnetizing forces remaining 
the same) a motion of any part through a distance dx 
results in a decrease of flux c/N, then the force resisting 
such motion will be proportional to dJU/dx. 

380. Law of the Electromagnet. — Before the law of the 

magnetic circuit was understood many attempts were made to 
find algebraic formulae to express the relation between the 
strength of current and the amount of magnetism produced. 
Lenz and Jacobi suggested that the magnetism of an electro- 
magnet loas proportional to the current and to the number of 
turns of 10 ire in the coil — in other words, is proportional to the 
ampere-turns. Or in symbols 

m = oCS, 
where a is a constant depending on the quantity, quality, and 
form of iron. This rule is, however, only true when the iron 
core is still far from being " saturated." If the iron is already 
strongly magnetized a current twice as strong will not double 
the magnetization in the iron, as Joule showed in 1847. 

Miiller gave the following approximate rule: — The strength 
of an electromagnet is proportional to the angle whose tangent 
is the strength of the niagnetizing current; or 

m = A tan -i C, 

where C is the magnetizing current, and A a constant depend- 
ing on the construction of the particular magnet. If the student 
will look at Fig. 121 and imagine the divisions of the horizontal 
tangent line OT to represent strengths of current, and the 
number of degrees of arc intercepted by the oblique lines to 
represent strengths of magnetism, he will see that even if OTbe 
made infinitely long, the intercepted angle can never exceed 90°. 
Another formula, known as Frolich's, is — 

where a and b are constants depending on the form, quality, and 
quantity of the iron, and on the winding of the coil. The con- 
stant b is the reciprocal of that number of amperes which would 
make m equal to half possible maximum of magnetism. 

The author's variety of this formula expresses the number of 
magnetic lines N proceeding from the pole of the electromagnet — 

N = Y— ^, 

C+C' 



374 



ELECTRICITY AND MAGNETISM part ii 



where Y represents the maximum number of magnetic lines that 
there would be if the magnetizing current were indefinitely in- 
creased and the iron core saturated, and C stands for that number 
of amperes which would bring the magnetism up to half-satura- 
tion. 

None of these empirical formulae are as useful as the rational 
formula at the end of Art. 377. 



Lesson XXXI. — Electromagnets 

381. Electromagnets. — In 1820, almost immediately 
after Oersted's discovery of the action of the electric cur- 
rent on a magnet needle, Arago and Dav}- independently 
discovered how to magnetize iron and steel by inserting 
needles or strips into spiral coils of copper wire around 




which a current was cumulating. The method is shown 
in the simple diagram of Fig. 187, w^here a current from 
a single ceU is passed through a spii-al coil of insulated 
copper wu'e, in the hollow of which is placed a strip of 
iron or steel, which is thereby magnetized. The separate 
turns of the coil must not touch one another or the 
central bar, otherwise the current will take the shortest 
road open to it and will not traverse the whole of the 
coils. To prevent such short-circuiting by contact the 




CHAP. V STURGEON'S ELECTROMAGNET 375 

wire of the coil should be overspun with silk or cotton 
(in the latter case insulation is improved by varnishing it 
or by steeping the cotton covering in melted paraffin wax), 
or covered with a layer of guttapercha. If the bar be of 
iron it will be a magnet only so long as the current flows ; 
and an iron bar thus surrounded with a coil of wire for 
the purpose of magnetizing it by an electric current is 
called an Electromagnet. Sturgeon, who gave this name, 
applied the discoveries of Davy and Arago to the con- 
struction of electromagnets far more power- 
ful than any magnets previously made. 
His first electromagnet was a horse-shoe 
(Fig. 188) made of a rod of iron about 
1 foot long and ^ inch in diameter 
coiled with a single stout copper wire 
of only 18 turns. With the current from iijjJIipjM 
a single cell it lifted 9 lbs. ; but with a 

Fiff 188 

more powerful battery it lifted 50 lbs. It 
was first shown by Henry that when electromagnets are 
required to work at the distant end of a long line they 
must be wound with many turns of fine wire. The 
great usefulness of the electromagnet in its application 
to electric bells and telegraphic instruments lies in the 
fact that its magnetism is under the control of the current; 
when circuit is " made " it becomes a magnet, when 
circuit is " broken " it ceases to act as a magnet. More- 
over, it is capable of being controlled from a distance, the 
current being " made " or " broken " at a distant point of 
the circuit by a suitable key or " switch." 

382. Polarity and Circulation of Current. — By apply- 
ing Ampere's Rule (Art. 197) we can find which end of 
an electromagnet will be the N-seeking pole ; for, imagin- 
ing ourselves to be swimming in the current (Fig. 187), 
and to face towards the centre where the iron bar 
is, the N-seeking pole will be on the left. It is con- 
venient to remember this relation by the following rules : 
— Looking at the S-seeking pole of an electromagnet, the 



376 



ELECTRICITY AND MAGNETISM part ii 





Fi^. 189. 



magnetizing currents are circulating round it in the same 
cyclic direction as the hands of a clock move ; and, looking 
at the N-seeking pole of an electromagnet, the magnetizing 
currents are circulating round it in the opposite cyclic 
direction to that of the hands 
of a clock. Fig. 189 shows 
this graphically. These rules 
are true, no matter whether 
the beginning of the coils is 
at the end near the observer, 
or at the farther end from 
him, i.e. whether the spiral be a right-handed screw, or 
(as in Fig. 187) a left-handed screw. It v/ill be just the 
same thing, so far as the magnetizing power is concerned, 
if the coils begin at one end and run to the other and 
back to where they began ;' or they 
may begin half-way along the bar and 
run to one end and then back to the 
other : the one important thing to 
know is which way the current flows 
round the bar when you look at it 
end-on. The corkscrew rule (Art. 
198) leads to the same result. 

Suppose an iron core to be wound 
with a right-handed coil, and that a 
current is introduced at some point, 
and to flow both ways, it will produce 
oppositely-directed magnetizing actions in the two points, 
and there will be consequent poles (Art. 120) at the point 
of entrance. In Fig. 190 an iron ring with a right- 
handedly wound closed coil is shown. There will be a 
double S pole at the point where the current enters, and 
a double X pole where it leaves the windings. 

383. Construction of Electromagnets. — The most 
useful form of electromagnet is that in which the iron 
core is bent into the form of a horse-shoe, so that both 
poles may be applied to one iron armature. In this 




Fig. 190. 




CHAP. V FORMS OF ELECTROMAGNETS 377 

case it is usual to divide the coils into two parts wound 
on bobbins, as in Figs. 6i and 191. The electromagnet 
depicted in Fig. 192 is of a form adapted for laboratory 
experiments, and has movable coils which are slipped on 
over the iron cores. The cores are united at the bottom 
by a stout iron yoke. Sometimes only one coil is wound 
on the yoke part. A special 
form of electromagnet de- 
vised by Ruhnikorff for ex- 
periments on diamagnetism 
is shown in Fig. 182. 

Many special forms* of 
electromagnet have been de- 
vised for special purposes. 
To give a very powerful 
attraction at very short dis- 
tances, a short cylindrical 
electromagnet surrounded by Fi"-.~191, 

an outer iron tube, united at 

the bottom by iron to the iron core, is found best ; the 
iron jacket constituting a return path for the magnetic 
Imes. This form is known as an iron-clad magnet. To 
attract iron across a wide gap which offers much reluc- 
tance, a horse-shoe shape with long cores should be chosen ; 
for it needs long cores to wind on enough wire to provide 
sufficient exciting power to drive the flux across the gap. 
To give a gentle pull over a long range a solenoid (Art. 
385), or long tubular coil, having a long movable iron core 
is used. For giving a very quick-acting magnet the coils 
should not be wound all along the iron, but only round 
the poles. As a rule the iron parts, including the yoke 
and armature, should form as nearly as possible a closed 
magnetic circuit. The cross-sections of yokes should be 
thicker than those of the cores. 

* For descriptions of these, as well as for discussion of all other matters 
relating to the subject, see the author's treatise on The Electromagnet and 
Electromagnetic Mechanism. 



378 



ELECTRICITY AND MAGNETISM part ii 



384. Lifting-power of Electromagnets. — The trac- 
tive force of an electromagnet depends not only on its 
magnetic strength, but also upon its form, and on the 



^^T 




Fig. 192. 



shape of its poles, and on the form of the soft iron 
armature which it attracts. It should be so arranged 
that as many lines of force as possible should run through 
the armature, and the armature itself should contain a 
sufficient mass of iron. Joule designed a powerful elec- 
tromagnet, capable of supporting over a ton. The 
maximum attraction he could produce between an electro- 
magnet and its armature was 200 lbs. per square inch, or 
about 13,800,000 dynes per square centimetre. Bidwell 
has found the attraction to go up to 226-3 lbs. per square 



cm^p. V LAW OF MAGNETIC TEACTION 



379 



inch when the wrought iron core was saturated up to 
19,820 magnetic lines to the square centimetre. The 
law of traction is that the pull per square centimetre is 
proportional to the square of the number of lines per 
square centimetre : or in symbols 



P = 



B2A 

Stt' 



where P is the pull in dpies, and A the area in square 
centims. In the following table are given the values of 
the tractive force for different stages of magnetization. 



B 


Dynes 


Grammes 


Pounds 


lines per 


per 


per 


per 


sq. cm. 


sq. centim. 


sq. centim. 


sq. inch. 


1.000 


39,790 


40-56 


■577 


2,000 


159,200 


162-3 


2-308 


3,000 


358,100 


365-1 


5-190 


4,000 


636,600 


648-9 


9-228 


5,000 


994,700 


1,014 


14-39 


6,000 


1,432,000 


1,460 


20-75 


7,000 


1,950,000 


1,987 


28-26 


8,000 


2,547,000 


2,596 


36-95 


9,000 


3,223,000 


3,286 


46-72 


10,000 


3,979,000 


4,056 


57-68 


12.000 


5,730,000 


5,841 


83-07 


14,000 


7,800,000 


7,950 


113-1 


16,000 


10,170,000 


10,390 


147-7 


18,000 


12,890,000 


13,140 


186-8 


20,000 


15,920,000 


16,230 


230-8 



It will be noted that doubling B makes the pull four 
times as great. One curious consequence of this law is 
that to enlarge its poles weakens the pull of an electro- 
magnet or magnet. In some cases — bar magnets for 
example — their tractive power is increased by filing 
down or rounding the poles so as to concentrate B. 



380 ELECTRICITY AND MAGNETISM part ii 

385. Solenoid. — Without any central core of iron 
or stee] a spiral coil of wire traversed by a current acts as 
an electromagnet (though not so powerfully as when an 
iron core is placed in it). Such a coil is sometimes termed 
a solenoid. A solenoid has two poles and a neutral 
equatorial region. Ampere found that it will attract 
magnets and be attracted by magnets. It will attract 
another solenoid; it has a magnetic field resembling 

generally that of a 
bar magnet. If so 
P9 arranged that it can 

turn round a verti- 
cal axis, it will set 
I itself in a IsTorth 

meridian. Fig. 193 
shows a solenoid ar- 
ranged with pivots, by which it can be suspended to a 
"table," like that shown in Fig. 198. 

With an iron core the solenoid becomes far more 
powerful. The effect of the iron core is by its greater 
permeability to multiply the number of magnetic lines 
as well as to concentrate them at definite poles. The 
student has been told (Art. 202) that the lines of force due 
to a current flowing in a wire are closed curves, approxi- 
mately circles (Figs. 115 and 195), round the wire. If 
there were no iron core many of these little circular lines 
of force would simply remain as small closed curves 
around their own wire ; but, since iron has a permeability 
hundreds of times greater than air, wherever the wire 
passes near an iron core the magnetic lines alter their shape, 
and instead of being little circles around the separate 
wires, run through the iron core from end to end, and 
round outside from one end of the coil back to the other. 
A few of the magnetic lines do this when there is no iron ; 
almost all of them do this when there is iron, and when 



CHAP. V EIELD INSIDE SOLENOID 381 

there is iron there are more lines to flow back.* Hence 
the electromagnet with its iron core has enormously 
stronger poles than the spiral coils of the circuit would 
have alone. 

In Art. 342 it was shown that the intensity of the 
magnetic field down the middle of a solenoid of length Z, 
having S spirals, carrying C amperes, is — 

10 I 

Since the area enclosed is irr^, the flux down the 
solenoid (without iron) will be 

N = 4^xCS. 
10/ 

And, since 47r magnetic lines go to one unit of mag- 
netism, the solenoid (without iron) will act as though 
it had as the magnetism at its pole — 

m = CS. 

10/ 

It will be noticed that for any solenoid of given length 
and radius the three magnetic quantities H (internal 
field), N (magnetic flux), and m (strength of poles) are 
proportional to the amperes of current and to the number 
of turns in the coil. The product which thus comes 
into all electromagnet formulae is called the number of 
ampere-turns. 

A solenoid with a movable iron plunger is sometimes 
called a sucking-magnet. The iron core tends to move into 
the position in which it best completes (Art. 379) the 
magnetic circuit. If the core is much longer than the 
coil, the pull increases as the end of the core penetrates 

* But, in the case of a permanent steel horse-shoe magnet, bi'inging up 
the u-on keeper, though it concentrates the lines through the poles, does 
not increase the total number of lines through the bend of the U". 



382 ELECTRICITY AND MAGNETISM part ii 

down the coil, diminishing quickly as the core emerges. 
Short iron cores are only pulled while at the mouth of 
the coil ; the maximum pull being when about half their 
length has entered. 

386. The Winding of Electromagnets. — The exact 
laws governing the winding of electromagnets are some- 
what complicated; but it is easy to give certain rules 
which are approximately true. Every electromagnet 
shows the same general set of facts — that with small 
exciting power there is little magnetism produced, with 
larger exciting power there is more magnetism, and that 
with very great exciting power the iron becomes prac- 
tically saturated and will take up very little additional 
magnetism. It follows at once that if the electromagnet 
is destined to be used at the end of a long line through 
which only a small current (perhaps only ^^^ ampere) 
will flow, the requisite number of ampere-turns to excite 
the magnetism will not be attained unless many turns of 
wke are used; and as the current is small a fine wire 
may be used. 

It may be noted that when electromagnets are wound 
with many turns of fine wire, these coils will add to the 
electric resistance of the circuit, and will tend to diminish 
the current. Herein lies a difference in construction of 
telegraphic and other instruments ; for while electro- 
magnets with " long coils," consisting of many turns of 
fine wire, must be used on long circuits where there is 
great line resistance, such an instrument would be of no 
service in a laboratory circuit of very small resistance, 
for the resistance of a long thin coil would be dispro- 
portionately gTeat : here a short coil of few turns of 
stout wire would be appropriate (see Art. 192). 

It is the nature of the line, according to whether it is 
of high resistance or low, which governs the questions 
how the coil shall be wound and how the battery shall 
be grouped. 

Similar electromagnets of different sizes must have 



CHAP, r WINDIXG OF ELECTROMAGNETS 383 

ampere-turns proportional to their linear dimensions if 
they are to be raised to equal degree of saturation. 

As the magnetism of the magnet depends on the 
number of ampere-turns, it should make no matter 
whether the coils are bigger than the core or whether 
they enwrap it quite closely. If there were no magnetic 
■leakage this would bfe true in one sense ; but for an equal 
number of turns large coils cost more and offer higher re- 
sistance. Hence the coils are wound as closely to the iron 
core as is consistent with good insulation. Also the iron 
is chosen as thick as possible, as permeable as possible, 
and formiug as compact a magnetic circuit as possible, so 
that the magnetic resistance may be reduced to its utmost, 
giving the greatest amount of magnetism for the number 
of ampere-turns of excitation. This is why horse-shoe- 
shaped electromagnets are more powerful than straight 
electromagnets of equal weight; and why also a horse- 
shoe electromagnet will only lift about a quarter as much 
load if one pole only is used instead of both. 

As the coils of electromagnets grow hot with the 
current, sufficient cooling surface must be allowed, or 
they may char their insulation. Each square centimetre 
of surface warmed 1° C. above the surrounding air can 
get rid of about 0-0029 watt. If 50° above the sur- 
rounding air be taken as the safe limit of rise of tem- 
perature, and the electromagnet has resistance r and 
surface s sq. cms., the highest permissible current will be 
0-38 ^/s/r amperes. 

387. Polarized Mechanism. — An electromagnet 
moves its armature one way, no matter which way the 
current flows. Reversing the current makes no difference. 
There are, however, two ways of making a mechanism 
that will cause an armature to move in either sense at 
will, (a) The armature's movement is controlled by 
an adjusted spring so as to be in an intermediate position 
when a weak current is flowing. Then sending a stronger 
current will move the armature one way, and weakening 



384 ELECTRICITY AND MAGNETISM pakt ii 

or stopping the current will make it move the other way. 
(6) A polarized armature or tongue {i.e. one that is in- 
dependently magnetized) is placed between the poles of the 
electromagnet instead of opposite them. The direction 
in which it tends to move will be reversed by reversing 
the current in the circuit of the electromagnet. 

388. Growth of Magnetism. — It requires time to 
magnetize an iron core. This is mainly due to the fact 
that a current, when first switched on, does not instantly 
attain its full strength, being retarded by the self-induced 
counter-electromotive-force (Art. 458) ; it is partly due to 
the presence of transient reverse eddy-currents (Art. 457) 
induced in the iron itself. Faraday's large electromagnet 
at the Royal Institution takes about two seconds to attain 
its maximum strength. The electromagnets of large 
dynamo machines often take ten minutes or more to rise 
to their working stage of magnetization. 

When electromagnets are used with rapidly alternating 
currents (Art. 470) there are various different pheno- 
mena, for which the student is referred to Art. 477. 



Lesson XXXII. — Electrodynamics 

389. Electrodynamics. — In 1821, almost immedi- 
ately after Oersted's discovery of the action of a current 
on a magnet. Ampere discovered that a current acts upon 
another current, apparently attracting it * or repelling it 
according to certain definite laws. These actions he in- 
vestigated by experiment, and from the experiments he 
built up a theory of the force exerted by one current on 
another. That part of the science which is concerned 
with the force which one current exerts upon another 
he termed Electrodynamics. It is now known that these 

* It would be more correct to speak of the force as acting on conductors 
carrying currents, than as acting on the currents themselves. 



CHAP. V MAGNETIC FIELD AROUND CURRENTS 385 

actions are purely magnetic, and are due to stresses in the 
intervening medium. The magnetic field around a single 
conductor consists of a magnetic whirl (Art. 202), and 
any other conductor carrying a current when brought 
into the field of the first is acted upon by it. Fig. 194 
shows the field due to two parallel straight current con- 




Fig. 194. 




ductors, which were passed through holes in a sheet of 
glass on which iron filings were sprinkled. In Fig. 194 
the currents flow in the same direction ; in Fig. 195 in 
opposite directions. In the first case the stresses in the 
field (Art. 119) tend to pull them together, in the second 
to push them apart.* 

390. Laws of Parallel and Oblique Circuits. — The 
following are the laws discovered by Ampere : — 

(i.) Two parallel portions of a circuit attract one another 
if the currents in them are flowing in the same direction, and 
repel one another if the currents flow in opposite directions. 

This law is true whether the parallel wires be parts of 
two different circuits or parts of the same circuit. 
The separate turns of a spiral coil, like Fig. 193, 
when traversed by a current attract one another ; 
such a coil, therefore, shortens when a current is 
sent through it. But this is equally well explained 

* See article by the author in the Philosophical Magazine. November 
18T8, p. 348. 

2c 



386 



ELECTRICITY AND MAGNETISM paet ii 



by the general law of electromagnetic systems 
(Art. 379), because shortening will reduce the 
reluctance of the magnetic circuit and increase 
the flux. 

(ii.) Two portions of circuits crossing one another obliquely 
attract one another if both the currents run either towards or 
from the point of crossing, and rejM one another if one runs 
to and the other from that point. 

Fig. 196 gives three cases of attraction and two of re- 
pulsion that occur in these laws. 

(iii.) When an element of a circuit exerts a force on 
another element of a circuit, that force always tends to urge 





Fig. 196. 

the latter in a direction at right angles to its own direction. 

Thus, in the case of two parallel circuits, the force of 

attraction or repulsion acts at right angles to the currents 

themselves. 

An example of laws ii. and iii. is afforded by the case 
showm in Fig. 197. Here two currents ab and cd 
are movable round O as a centre. There will be 
an apparent repulsion between a and d and be- 
tween c and b, while in the other quadrants there 
will be an apparent attraction, a attracting c, and 
b attracting d. 



CHAP. V ATTRACTIONS OF CURRENTS 



387 



The foregoing laws may be summed up in one, 
by saying that two portions of circuits, however 
situated, set up stresses 
in the surrounding- 
medium tending to set 
them so that their cur- 
rents flow as nearly in 
the same path as 
possible. 

(iv.) The force exerted be- 
tween two parallel portions of circuits is proportional to the 
product of the strengths of the two currents, to the length of 
the portions, and inversely proportional to the simple distance 
between them. 

391. Ampere's Table. — In order to observe these 
attractions and repulsions, Ampere devised the piece of 




Fi^. 197. 




Fig. 198. 

apparatus known as Ampere's Table, shown in Fig. 198, 
consisting of a double supporting stand, upon which 
wires, shaped in different ways, can be so hung as to be 
capable of rotation. The ends of the suspended wires 



388 



ELECTRICITY AND MAGNETISM part ii 



dip into two mercury cups, so as to ensure good contact, 
while allowing freedom to move. 

By the aid of this piece of apparatus Ampere further 
demonstrated the following points : — 

(a) A circuit doubled back upon itself, so that the current 

flows back along a path close to itseK, exerts no force 

upon external points. 
(6) A circuit bent into zig-zags or sinuosities produces the 

same magnetic effects on a neighbouring piece of circuit 

as if it were straight. 

(c) There is in no case any force tending to move a conduc- 
tor in the direction of its own length. 

(d) The force between two conductors of any form is the 
same, whatever the linear size of the system, provided 
the distances be increased in the same proportion, and 
that the currents remain the same in strength. 

The particular case, given in Fig. 199, will show the value of 
these experiments. Let AB and CD represent two wires carry- 
ing currents, lyiug neither parallel nor in the same plane. It 
follows from (&) that if w^e replace the portion PQ by the crooked 




Fig. 199. 

wire PRSQ, the force will remain the same. The portion PR is 
drawn verticallj- downwards, and as it can, by (c) , experience no 
force in the direction of its length, this portion will neither be 
attracted nor repelled by CD. In the portion RS the current runs 
at right angles to CD, and this portion is neither attracted nor 
repelled by CD. In the portion SQ the current runs parallel to 
CD, and in the same direction, and will therefore be attracted 
downwards. On the whole therefore, PQ will be urged towards 



CHAP. V ELECTRODYNAMIC THEORY 389 

CD. The portions PR and RS will experience forces of rotation, 
however, P being urged round R as a centre towards C, and R 
being urged horizontally round S towards C. These actions 
would tend to make AB parallel with CD. 

392. Ampere's Theory. — From the four preceding 
experimental data, Ampere built up an elaborate mathe- 
matical theory, assuming that, in the case of these forces 
acting apparently at a distance across empty space, the 
action took place in straight line^ between two points, 
the total attraction being calculated as the sum of the 
separate attractions on all the different parts. 

The briefest summary must suffice. If we deal first with 
two piarallel elements of length cUi and dl2 carrying currents 
C1C2, and set at right angles to the distance r joining them, 
their mutual force will be 

df = - CiC2C?^i(??2/100r2. 

If, however, they are not parallel or in one plane, let <f) be 
the angle they make with one another, while Oi and 0.2 are the 
angles they make with 7- ; when 

df=— CiC2dhdl2iGOS <}> — i cos ^j-cos 02)/lOOr2. 

By integrating this expression one obtains the forces for 
circuits of any given dimensions. For example, for two parallel 
straight conductors of lengths I1I2, if these lengths are great 
compared with the distance r between them, we have 

/=-2CiC2V2/100r. 

The researches of Faraday have, however, led to other 
views; the mutual attractions and repulsions being re- 
garded as due to actions taking place in the medium 
which fills the space around and between the conductors. 
All these so-called electrodynamic actions are merely 
magnetic actions. 

An interesting experiment, showing an apparent 
mutual self-repulsion between contiguous portions of the 
circuit, was devised by Ampere. A trough divided by 
a partition into two parts, and made of non-conduct- 
ing materials, is filled with mercury. Upon it floats a 



390 



ELECTRICITY AND MAGNETISM part ii 



metallic bridge formed of a bent wire, of the form shown 
in Fig. 200, or consisting of a glass tube filled siphonwise 
with mercury. When a current is sent through the 




riff. 200. 



floating conductor from X over MN, and out at Y, the 
floating bridge is observed to move so as to increase the 
area enclosed by the circuit. But the force would be 
diminished indefinitely if the two parallel 
parts could be made to lie quite close to 
one another. 

393. Electromagnetic Rotations. — 
Continuous rotation can be produced 
between a magnet and a circuit, or be- 
tween two parts of one circuit, provided 
that one part of the circuit can move 
while another p>art remains fixed, or that 
the current in one part can be reversed. 
The latter device is adopted in the con- 
struction of electric motors (Art. 443). 
The former alternative is applied in 
some historic apparatus for showing 
rotations, a sliding-contact being made 
between one part of the circuit and 
another. Several different forms of rotation-apparatus 
were devised by Faraday and by Ampere. One of 
Faraday's is shown in Fig. 201, in which a wire carrying 
a current is jointed at the top and dips into a cup of 




CHAP. V ELECTRODYNAMOMETERS 391 

mercury surrounding the pole of a magnet. On switching 
on the current the wire at once begins to walk round the 
pole with a motion that continues until the current is 
switched off. 

A pole of a magnet can also be made to rotate round 
a current; and if a vertical magnet be pivoted so as to 
turn around its own axis it will rotate when a current is 
led into its middle region and out at either end. If the 
current is led in at one end and out at the other there 
will be no rotation, since the two poles would thus be 
urged to rotate in opposite ways. Liquid conductors too 
can exhibit electromagnetic rotations. Let a cylindrical 
metallic vessel connected to one pole of a battery be 
filled with mercury or dilute acid, and let a wire from 
the other pole dip into its middle, so that a current may 
flow radially from the centre to the circumference, or 
vice versa ; then, if this be placed upon the pole of a 
powerful magnet, or if a magnet be held vertically over 
it, the liquid may be seen to rotate. 

394. Electrodynamometer. — Weber devised an in- 
strument known as an electrodynamometer for measuring 
the strength of currents by means of the electrodynamic 
action of one part of the circuit upon another part. It 
is a sort of galvanometer, in which, instead of a needle, 
there is a small coil suspended. One form of this instru- 
ment, in which both the large outer and small inner coils 
consist of two parallel coils of many turns, is shown in 
Fig. 202. The inner coil CD is suspended with its axis 
at right angles to that of the outer coils A A, BB, and is 
supported hijilarly (see Art. 130) by two fine metal wires. 
If one current flows round hotli coils in either direction the 
inner bobbin tends to turn and set its coils parallel to 
the outer coils ; the sine of the angle through which the 
suspending wires are twisted being proportional to the 
square of the strength of the current. 

If G be the " principal constant " (Art. 213) of the large coils, 
and ,7 the " moment " of the small coils (Art. 34^6) when carrying 



392 



ELECTRICITY AND MAGNETISM part ii 



unit current, and C1C2 the currents in them, the torque (or turn- 
ing moment) will be 

=G^CiC2/100. 

The chief advantage of this instrument over a galvan- 
ometer is, that it may be used for alternating currents ; a 




Fig. 202. 



current in one direction being followed by a reverse 
current, perhaps thousands of times in a minute. Such 
currents hardly affect a galvanometer needle at all; the 
needle simply quivers in its place without turning. 

395. Siemens's Electrodynamometer. — In Siemens's 
dynamometer (Fig. 203), much used for measurement 
of strong currents, whether of the continuous or the 
alternating kind, one coil is fixed permanently, whilst 
the other coil, of one or two turns, dipping with its 
ends in mercury cups, is hung at right angles, and 
controlled by a spiral spring below a torsion-head. 



CURRENT BALANCES 



393 



When current passes the movable coil tends to turn 
parallel to the fixed coils, but is prevented ; the torsion 
index being turned until the twist on the spring balances 
the torque. The angle through which 
the index has had to be turned is 
proportional to the product of C^Cg, 
the currents in the fixed and movable 
coils. 

For use of dynamometer as watt- 
meter, see Art, 438. 

396. Kelvin's Current Balances. 
— Joule, ]\Iascart, Lord Ravleigh, and 
others have measured currents by 
balances in vs'hich gravity was opposed 
to the attraction or repulsion of two 
coils. Of such balances the most 
perfect are those of Lord Kelvin, the 
principle of which is outlined in Fig. 204. There are four 
fixed coils, ABCD, between which is suspended, by a 
flexible metal ligament of fine wires, at the ends of a 




Fig. 203. 




Fig. 204. 

light beam, a pair of movable coils, E and F. The 
current flows in such directions through the whole six 
that the beam tends to rise at F and sink at E. The 
beam carries a small pan at the F end, and a light arm, 
not shown in Fig. 204, but shown in Fig. 205, along 
which, as on a steel-yard, a sliding weight can be moved 
to balance the torque due to the current. The current is 
proportional to the square-root of this torque, since the 



394 ELECTEICITY AND MAGNETIS:sr part ii 




CHAP. V CURRENT BALANCES 395 

force is proportional to the product of the current in the 
fixed and movable coils as in all electrodynamometers. 

Lord Kelvin has designed a whole range * of these instru- 
ments : — a centi-ampere balance reading from O'Ol to 1 ampere ; 
a deci-ampere balance reading from 01 to 10; a deka-ampere 
balance reading from 1 to 100 ; a hekto-ampere balance reading 
from 6 to GOO ; and a kilo-ampere balance reading up to 2500 am- 
peres. The centi-ampere balance is shown in Fig. 205, in which 
the sliding weight is carried on the base of the pointer (shown 
white), and when at the zero of the scale just balances the weight 
in the Y-shaped pan . Any current passing througli the coils causes 
the beam to tilt and the pointer is moved (by means of a self- 
releasing slider attached to cords) until it is again horizontal (as 
shown by the black pointer at either end) . With a certain pair of 
weights the iixed scale gives the current in decimal parts of an 
ampere ; but by the use of other weights a wider range is obtained. 

The "ampere-standard" instrument, and the "volt- 
standard " instruments of the Board of Trade, kept at 
Whitehall as legal standards for Great Britain, embodying 
the international units, are current balances of special con- 
struction, designed by Major Cardew. 

397. Electromagnetic Actions of Convexion Currents. 
— According to Faraday a stream of particles charged 
with electricity acts magnetically like a true conduction 
current. This was first proved in 1876 by Rowland, who 
found a charged disk rotated rapidly to act upon a mag- 
net as a feeble circular current would do. Convexion 
currents, consisting of streams of electrified particles, are 
also acted upon by magnets. The convective discharges 
in vacuum-tubes (Art. 320) can be drawn aside by a 
magnet, or caused to rotate around a magnet-pole. The 
brush discharge (Art. 319) when taking place in a strong 
magnetic field is twisted. The electric arc (Art. 448) 
also behaves like a flexible conductor, and can be attracted 
or repelled laterally by a magnet. Two stationary posi- 
tively electrified particles repel one another, but two 

* For a fuller account of these Current Balances, and of the Wattmeters 
on the same principle, see Gray's Absolute Meastirements in Electricity 
and Magnetism, from which Fig'. 205 is taken. 



396 ELECTRICITY AXD ^lAGXETISM part ii 

parallel currents attract one another (Art. 390), and if 
electrified particles flowing along act like cm-rents, there 
should be an (electromagnetic) attraction between, two 
electrified particles moving along side by side through 
space. According to Maxwell's theory (Art. 518) the 
electrostatic repulsion will be just equal to the electro- 
magnetic attraction when the particles move with a velocity 
equal to the velocity of light. 

Hall discovered in 1879 that when a powerful magnet 
is made to act upon a current flowing along in a strip of 
very thin metal, the equipotential lines are no longer at 
right angles to the lines of flow of the cmTeut in the strip. 
This action appears to be connected with the magnetic 
rotation of polarized light (Art. 526). the coefficient of this 
transverse thrust of the magnetic field on the current 
being feebly -f in gold, strongly -|- in bismuth, and — in 
iron, and immensely strong negatively in tellm'ium. It 
was shown by the author, and about the same time by 
Righi, that those metals which manifest the HaU effect 
undergo a change in theu* electric resistance when placed 
in the magnetic field. The resistance of bismuth increases 
so greatly that it affords a way of measuring the strength 
of magnetic fields. 

398. Ampere's Theory of Magnetism. — Ampere, 
finding that solenoids (such as Fig. 193) act precisely as 
magnets, conceived that all magnets are simply collections 
of currents, or that around every individual molecule of 
a magnet an electric current is ceaselessly circulating. 
We know that such currents could not flow perpetually if 
there were any resistance to them, and we know that 
there is resistance when electricity flows fi'om one mole- 
cule to another. As we know nothing about the interior 
of molecules themselves, we cannot assert that Ampere's 
supposition is impossible. Since a whirlpool of electricity 
acts like a magnet, there seems indeed reason to think 
that magnets may be merely made up of rotating portions 
of electrified matter. 



CHAPTER yi 

MEASUREMENT OF CURRENTS, ETC. 

Lesson XXXIII. — Ohm's Law and its Consequences 

399. Law of Dr. Ohm. —In Art. 191 the law 
discovered by Dr. G. S. Ohm was stated in the following 
terms : — The strength of the current varies directly as the 
electromotive-force, and inversely as the resistance of the 
circuit. 

Using the units adopted b}^ practical electricians, and 
explained in Art. 3.54, we may now restate Ohm's law in 
the following definite manner: — The number of amperes 
of current flowing through a circuit is equal to the number of 
volts of electromotive-force divided by the number of ohms of 
resistance. Or, 

amperes = volts ^ ohms, 

C = E/R. 

The above is the simplest way of stating the law, but 
in its application it is not quite so simplg. If we apply 
it to a whole circuit we mast consider both the total E 
and the total R. For if a number of cells are used and 
the circuit be made up of a number of different parts 
through all of which the current must flow, we have to 
take into account not only the electromotive-forces of the 
cells, but their resistances, as well as the resistances of 
397 



398 ELECTRICITY AND MAGNETISM part ir 

other parts of the circuit. For example, the current may 
flow from the zinc plate of the first cell through the liquid 
to the carbon plate, then through a connecting wire or 
screw to the next cell, through its liquid, through the con- 
necting screws and liquids of the rest of the cells, then 
through a wire to a galvanometer, then through the coils 
of the galvanometer, then perhaps through an electrolytic 
cell, and finally through a return wire to the zinc pole of 
the battery. In this case there are a number of sepai-ate 
electromotive-forces all tending to produce a flow, and a 
number of different resistances, each obstructing the flow 
and adding to the total resistance. If in such a case we 
knew the separate values of all the different electromotive- 
forces and all the different resistances that are in series 
we could calculate what the current would be, for it would 
have the value — 



eJ + e" + e'" + e^^ + 



C 



r' + r" + r'" + r^^ + • • 
Total electromotive-force 



Total resistance 



Example. — Let there be 5 cells in series each having e — 
1-4 volts, and each an internal r = 0-4 ohm ; and let the 
external part of circuit have resistance 3 ohms. Total 
E = 7 volts ; total R = 5 ohms. Current C will be If 
amperes. 

If any one of the cells were set wrong way round its 
electromotive-force would oppose that of the other cells ; 
an opposing electromotive-force must therefore be sub- 
tracted, or reckoned as negative in the algebraic sum. 
The " polarization " (Arts. 175 and 487) which occurs 
in battery cells and in electrolytic cells after working 
for some time is an opposing electromotive-force, and 
diminishes the total of the electromotive-forces in the 
circuit. So, also, the induced back E.M.F. which is set 
up when a current from a battery drives an electric 
motor (Art. 444) reduces the strength of the working 



CHAP. VI OHM'S LAW 399 

current; in such case, if E is the electromotive-force of 
the battery, e the opposing electromotive-force, and R the 
total resistance, we shall have 

r^ E — e 



Example. — Suppose the battery to generate current at 25 
vohs, and the motor to generate a back electromotive- 
force of 20 volts, and the total resistance to be 21 ohms, 
there will be a current of 2 amperes. 

But we may apply Ohm's law to a part of a circuit. 
If e represents the difference of potential between two 
ends of a conductor of resistance r, the current C in it 
must be = e/r. Or, to put it the other way round, the 
electromotive-force needed to drive C amperes through a 
resistance of r ohms will be e = rC volts. 

Consider the case of a circuit of which the resistance 
is made up of two parts, an external resistance E, consist- 
ing of wires, lamps, etc., and of a smaller resistance r inter- 
nal to the battery or dynamo (viz. the resistance of the 
liquids in the cells, or of the wire of the armature). Then 
if E is the whole electromotive-force we shall have as 
current 

C- ^ 

or C(R + r) = E', 

or again CR + Cr = E. 

This means in words that the total volts may be considered 
as being employed partly in driving the current through 
the external resistance R, partly in driving the current 
through the internal resistance r. This latter part 
of the electromotive-force is called the lost volts; the 
remainder being the useful or externally available volts, 
that would be m.easurable by a voltmeter (Art. 220) set 
across the terminals. If we call the available volts V we 
may write V = CR, whence 



400 ELECTRICITY AND MAGNETISM part ii 

V = E-Cr; 

or in words : the volts as measured at the terminals of a 
cell or dynamo are less than the whole E.M.F. generated 
therein ; being equal to the whole E.M.F. less the lost 
volts. The lost volts being proportional to internal 
resistance it is obviously best to keep all internal resist- 
ances as low as possible. Only when the cell is giving no 
current are the external volts V equal to the whole E.M.F. ; 
for when C = o, Or is also = o. 

Example. — A. dynamo is designed to generate its currents 
with an electromotive-force of 105 volts. Tlie internal 
resistance of its armature is sc? ohm. When it is giving 
out current of 120 amperes, the lost volts will be 120 X 35 
= 4 volts. Consequently the volts available in the exter- 
nal circuit will be only 101. 

Since C = -^ = X it follows also that V = E ^ 



R + r R R + r 

400. Resistance. — Resistance is the name given to 
that property of materials by virtue of which they obstruct 
the steady flow of electricity through them, and fritter 
down into heat the energy of the current. It is found 
that the resistance of a metal wire, if kept at an unvary- 
ing temperature, is the same whether a large current or 
a small current be flowing through it. For example, if 
a wire has a resistance such that when a diiference of 
potential of 10 volts is applied to its ends a current of 2 
amperes flows through it (its resistance being 5 ohms), 
it will be found that if 1 volt is applied the current will 
be 0.2 amperes, the ratio between volts and amperes 
being 5 as before. 

The unit of resistance, or ohm, is a standard chosen in 
order that the resistances of other conductors may be 
expressed in definite numbers. The definition of it is 
given in Art. 354. It is convenient to remember that 
100 yards of ordinary iron telegraph-wire has roughly a 
resistance about 1 ohm. 



CHAP. Ti RESISTANCES 401 

Resistances in a circuit may be of two kinds — first, 
the resistances of the conductors (metals, alloys, liquids) 
themselves ; second, the resistances due to imperfect contact 
at points. The latter kind of resistance is affected by 
pressure, for when the surfaces of two conductors are 
brought into more intimate contact with one another, 
the current passes more freely from one conductor to the 
other. The contact-resistance of two copper conductors 
may vary from infinity down to a small fraction of an 
ohm, according to the pressure. The variation of resist- 
ance at a point of imperfect contact is utilized in telephone 
transmitters (Art. 512). The conduction of powdered 
metals is remarkable. A loose heap of filings scarcely 
conducts at all, owing to the want of cohesion, or to the 
existence of films of air or dust. But it becomes instantly 
a good conductor if an electric spark is allowed to occur 
anywhere within a few yards of it (see Art. 521). The 
resisting films of air are broken down by minute internal 
discharges in the mass. A very slight agitation by tap- 
ping at once makes the powder non-conductive. 

For the purpose of regulating the flow of currents, 
and for electrical measurements (Art. 411), variable 
resistances are employed. Resist- 
ance coils (Art. 414) are sets of 
coils made each of a definite 
value in ohms, of which one or 
more can be inserted in the 
cii'cuit at will. Rheostats consist 
of easily-adjustable resistances, 
the length of wire in circuit 

being varied by turning a handle. In some cases the 
rheostat wire is wound off and on to a roller. In 
others a handle (Fig. 206) moving over a number of 
metal studs varies the amount of resistance-wire through 
which the current must flow. Carbon rheostats consist of 
a number of little plates of hard carbon, about 3 inches 
square, arranged in a pile, with a screw to reduce their 
2d 




402 ELECTRICITY AND MAGNETISM part ii 

resistance by squeezing them together into better con- 
tact. 

401. Laws of Resistance. — The follo\Ying are the 
laws of the resistance of conductors: — 

(i .) The resistance of a conducting icire is proportional to 
its length. If the resistance of a mile of iron 
telegraph ^Yire be 17 ohms, that of 50 miles will 
be 50 X 17 = 850 ohms. 

(ii.) The resistance of a conducting wire is inversely pro- 
portional to the area of its cross-section, and therefore 
in the usual round wires is inversely proportional 
to the square of its diameter. Ordinary telegraph 
wire is about i of an inch thick; a wire twice 
as thick w^ould conduct four times as well, 
having four times the area of cross - section ; 
hence an equal length of it w ould have only \ 
the resistance. 

(iii.) The resistance of a conducting icire of given length 
and thickness depends upon the material of which 
it is made — that is to say, upon the specific 
resistance of the material. 

If the length of a wire be I centimetres, and its area 
of section A square centimetres, and the specific resistance 
of the material be p, then its resistance R wall be 

E = /p/A. 

Example. — Find the resistance of a platinoid wire of sec- 
tion 0-OOi sq. cm., and 200 cm. long; p = 32-5 X 10-6. 
R = l-()25 ohms. 

402. Conductance and Resistance. — The term con- 
ductance is used as the inverse of resistance ; a conductor 
whose resistance is r ohms is said to have a coiiductance 
of \ /r ^'■mhos." When a number of conductors are in 
parallel with one another their united conductance is the 
sum of their separate conductances. 

The conductance of a prism of which the length is 



RESISTIVITY 403 



1 cm. and its area of section is 1 sq. cm., is called its 
conductivity or specific conductance. 

The resistance of a prism of length 1 cm. and section 
1 sq. cm. is sometimes called its resistivity or specific 
resistance. 

403. Specific Resistance. — The specific resistance of 
a substance is most conveniently stated as the resistance 
(in millionths of an ohm) of a centimetre cube of the 
substance. The Table on p. 404 also gives the relative 
conductance when that of copper is taken as 100 : — 

Aluminium is a better conductor than silver, weight 
for weight. 

It is found that those substances that possess a high 
conducting power for heat are also the best conductors 
of electricity, but the ratio of these conductivities is 
not constant ; it varies as the absolute temperature. 

Liquids fall under three heads : (1) molten metals and 
alloys, which conduct simply as metals; (2) fused salts 
and solutions of salts and acids, which conduct only hy 
electrolysis (Art. 487) ; (3) insulators, such as the oils, tur- 
pentine, etc., and bromine. Liquid electrolytes are worse 
conductors than metals ; gases, including steam, are per- 
fect non-conductors, except when so rarefied as to admit 
of discharge by convexion through them (Art. 320). 

404. Effects of Heat on Resistance. — Changes of 
temperature affect temporarily the conducting power 
of metals. ISTearly all the pure metals increase their 
resistance about 04 per cent for a rise of 1° C. in tem- 
perature, or about 40 per cent when warmed 100°. 
When cooled in liquid oxygen the resistance was found 
by Wroblewski to fall greatly. A copper wire which at 
0° had a resistance of 17-5 ohms fell to 1-65 ohms at 
— 201° C. Dewar and Fleming find all pure metals to 
lower their resistance as though at — 274° C. (absolute 
zero of temperature) they would become perfect con- 
ductors. The resistance of carbon, on the other hand, 
diminishes on heating. The filament of a glow-lamp, 



404 



ELECTRICITY AND MAGNETISM part ii 



TABLE OF SPECIFIC EESISTANCE. 



Substance. 


Specific 

Eesistance 

(microhms of 

1 cm. cube). 


Eesistance 

(ohms) of 

metre length 

1 sq. mm. 

Section. 


Eelative 
Conductance. 


Metals at 0° C. 
Copper (annealed) 

'• (hard) 
Silver (annealed) . 

" (hard) . 
Gold .... 
Aluminium (annealed) 
Platinum 
Iron (pure) . 
Iron (telegraph wire) . 
Lead .... 
Mercury 
Selenium 
Carbon (graphite) 

" (arc light) 


1-570 

1-603 

1-492 

1-620 

2-077 

2-889 

8-982 

9-638 
15 

19-63 
94-34 
6 X 1010 
2400 to 42000 
about 4000 




0157 

0160 

0149 

0162 

0208 

0289 

0898 

0964 

15 

1963 

9434 


100 

98-1 
105 

98 

76 

54 

17 

16 

10 
8^3 
1-6 
1 




40.000'000>000 


Alloys. 

German-silver 

(Cu 60, Zn 26, Ni 14) 
Platinum-silver 

(Pt 67, Ag 33) 
Platinoid 

(Cu 59, Zn 25-5, Ni 
14, W 55) 
Manganin 

(Cu 84, M 12, Mn 3-5) 


20-76 

2-4 

32-5 

47-5 


•2076 

-024 

•325 

•475 


7-6 
6-5 

4-8 

3^3 


Liquids at 18° C. 
Pure water . 
DUute H,S04. 5% 

" H2SO4,30% . 

" H2SO4, 80% . 

" ZnS04, 24% . 

" HNO3, 30% . 


26-5 X 108 
486 X 10* 
137 X 10* 
918 X 10* 
214 X 105 
129 X 10* 




less than one 
millionth part 


Insulators. 

Glass at 20° C. 
Glass at 200° C. . 
Guttapercha 24° C. 


91 X 1018 
22-7 X 1012 
4-5 X 1020 




less than one 
bilhonth 



INSULATOES 405 



which when cold was 230 ohms, was only 150 when white 
hot. German-silver and other alloys do not show so 
much change, hence they are used in making standard 
resistance coils. The temperature-coefficient of German- 
silver is only 0-00044 for 1° C, or j\ that of the pure 
metals. Platinoid and platinum-silver have about 0-00011 
for their coefficient. Weston has found alloys of man- 
ganese, copper, and nickel, which have a small negative 
coefficient. Those liquids which only conduct by being 
electrolyzed (Art. 234) conduct better as the tempera- 
ture rises. The effect of light in varying the resist- 
ance of selenium is stated in Art. 529. The property 
of changing resistance with temperature is now used 
for measuring furnace temperatures in Callendar's 
platinum pyrometer. The bolometer used by Langley 
in researches on radiant heat depends on the same 
property. 

405. Insulators. — The name insulators is given to 
materials which have such high resistances that they can 
be used as non-conductors. They differ much in their 
mechanical qualities as well as in their insulation-resist- 
ance. They may be classed under several heads : (1) 
Vitreous, including glass of all kinds and slags ; (2) Stony, 
including slate, marble, stoneware, steatite, porcelain, 
mica, asbestos ; (3) Resinous, including shellac, resin, bees- 
wax, pitch, various gums, bitumen, ozokerit ; (4) Elastic, 
including india-rubber, guttapercha, ebonite ; (5) Oily, 
including various oils and fats of animal and vegetable 
origin, as well as solid paraffin and petroleum oil ; (6) 
Cellulose, including dry wood and paper, and preparations 
of paper, such as "fibre" and celluloid. All these 
materials decrease their resistance enormously as the 
temperature rises, and in general become fairly good 
conductors as soon as any chemical change begins ; some 
of them (as glass) conduct as electrolytes so soon as 
they soften. 

The name insulators is also used for the insulating 



406 



ELECTRICITY AND MAGNETISM part ii 



supports of stoneware, porcelain, or glass on which tele- 
graph wires are carried (Art. 497). 

406. Typical Circuit. — Let us consider the typical 
case of the circuit shown in Fig. 207, in which a battery, 
ZC, is joined up in circuit with a galvanometer by means 
of wares whose resistance is R. The total electromotive- 
force of the battery we will call E, and the total internal 
resistance of the liquids in the cells r. The resistance of 
the galvanometer coils may be called G. Then, by Ohm's 
law: — 



C = 




R + r + G 

I'he internal resistance r of the liquids of the battery 
bears an important relation to the external resistance of 

the circuit (including E, 
and G), for on this relation 
depends the best way of 
arranging the battery cells. 
Suppose, for example, that 
we have a battery of 50 
small Daniell's cells at our 
disposal, of which we may 
reckon the electromotive- 
force as one volt (or, more 
accuratel}^, 1-07 volt) each, and each having an internal 
resistance of two ohms. If we have to use these cells on 
a circuit where there is already of necessity a high resist- 
ance, w^e should couple them up " in series " rather than 
in parallel. For, supposing we have to send our current 
through a line of telegraph 100 miles long, the external 
resistance R will be (reckoning 13 ohms to the mile of 
wire) at least 1300 ohms. Through this resistance a 
single such cell would give a current of less than one milli- 
ampere, for here E = 1, R = 1300, r = 2, and therefore 



Fiff. 207. 



1 



1 



R + r 1300 + 2 1302 
too weak to work a telegraph instrument. 



of an ampere, a current far 



CHAP. Ti CIRCUIT CALCULATIONS 407 

With fifty such cells in series we should have E = 50, 
r = 100, and then 

ri 50 50 1 J, o- -IT 

C = = = — of an ampere, or over 3o milli- 

1300 + 100 UOO 28 ^ 

amperes. In telegraph work, where the instruments 
require a current of 5 to 10 milli-ainperes to work them, 
it is usual to reckon an additional Daniell's cell for every 
5 miles of line, each instrument in the circuit being- 
counted as having as great a resistance as 10 miles of 
wire. 

If, however, the resistance of the external circuit be 
small, such arrangements must be made as will keep the 
total internal resistance of the battery small. Suppose, 
for example, we wish merely to heat a small piece of 
platinum wire to redness, and use stout copper wires to 
connect it with the battery. Here the external resist- 
ance may possibly not be as much as 1 ohm. In that 
case a single cell would give a current of ^ of an ampere 
(or 333 milli-amperes) through the wire, for here E = 1, 
R = 1, and r = 2. But 10 cells would only give half as 
much again, or 476 milli-amperes, and fifty cells only 
495 milli-amperes, and with an infinite number of such 
cells in series the current could not possibly be more 
than 500 milli-amperes, because every cell, though it adds 
1 to E, adds 2 to R. It is clear then that though link- 
ing many cells in series is of advantage where there is the 
resistance of along line of wire to be overcome, yet where 
the external resistance is small the practical advantage of 
adding cells in series soon reaches a limit. 

But suppose in this second case, where the external 
resistance of the circuit is small, we reduce also the 
internal resistance of our battery by linking cells to- 
gether in parallel, joining several zincs of several cells 
together, and joining also their copper poles together 
(as suggested in Art. 192), a different and better result 
is attained. Suppose we thus join up four cells. Their 
electromotive-force will be no more, it is true, than that 



408 ELECTRICITY AXD MAGNETISM part ii 



of one cell, but their resistance will be but i of one such 
cell, or ^ an ohm. These four cells would give a current 
of 666 miUi-amperes through an external resistance of 1 
ohm, for if E = 1, R = 1, and the internal resistance 

be i of r, or = i, then 

"p " 

C = — - — = I of an ampere, or 666 milli-amperes. 
R + ?' 
If we arrange the cells of a battery in n files of m 
cells in series in each file (there being m x n similar cells 
altogether), the electromotive-force of each file will be 
m times the electromotive-force E of each cell, or ynE ; 
and the resistance of each file will be m times the resist- 
ance r of each cell, or mr. But there being n files in 

parallel the whole internal resistance will be only - 

n 

of the resistance of any one file, or will be —r, hence, 

n 
by Ohm's law, such a battery would give as its current 
^ _ wE 
^r + R 

n 

407. Best Groupings of Cells. — If the question 
arises as to the best way of grouping a given number of 
cells, it must be replied that there are several best ways. 

(1) Grouping for best Economy. — So group the ceUs 
that their united internal resistance shall be very small 
compared with the external resistance. In this case 
the materials of the battery will be consumed slowly, and 
the current will not be drawn off at its greatest possible 
strength ; but there will be a minimum waste of energy 
(Art. 435). 

(2) Grouping for greatest Current. — It can be shown 
mathematically that, for a given battery of cells, the way 
of grouping them that will give the largest steady current 
when the}^ are required to work through a given external 
resistance R, is so to choose m and n that the internal 

resistance (— ?') shall equal the external resistance. The 



CHAP. Ti GROUPING OF CELLS 409 

student should verify this rule by taking examples and 
working them out for different groupings of the cells. 
Although this arrangement gives the strongest current it is 
not the most economical; for if the internal and external 
resistances be equal to one another, the useful work in 
the outer circuit and the useless work done in heating the 
cells will be equal also, half the energy being wasted. 

(3) Grouping for quickest Action. — If there are electro- 
magTiets, or other objects possessing self-induction (Art. 
458) in the circuit, which would tend to prevent the 
current rising quickly to its proper value, the best group- 
ing to cause the current to rise as quickly as possible is 
one that will make the internal resistance higher than the 
external, namely, put all the cells in series (see Art. 460). 

408. Long and Short Coil Instruments. — The stu- 
dent will also now have no difficulty in perceiving why 
a "long-coil" galvanometer, or a "long-coil " electromag- 
net, or instrument of any kind in which the conductor 
is a long thin wire of high resistance, must not be 
employed on circuits where both R and r are already 
small. He will also understand why, on circuits of great 
length, or where there is of necessity a high resistance and 
a battery of great electromotive-force is employed, " short- 
coil " instruments are of little service, for though they 
add little to the resistances, their few turns of wire are not 
enough to produce the required action with the small cur- 
rents that circulate in high-resistance circuits. He will 
understand, too, why " long-coil " instruments are here 
appropriate as multiplying the effects of the currents by 
their many turns, their resistance, though perhaps large, 
not being a serious addition to the existing resistances of 
the circuit. The main point to grasp is that it is the 
nature of the line, whether of high resistance or low, which 
determines not only the grouping of the battery, but also 
what kind of winding is appropriate in the instruments. 

409. Divided Circuits. — If a circuit divides, as in 
Fig. 208, into two branches at A, uniting together again 




410 ELECTRICITY AND MAGNETISM part ii 

at B, the current will also be divided, part flowing through 
one branch, part through the other. Any branch which 
serves as a by-pass to another branch is termed a shunt. 
The relative strengths of current in the two branches will be 

proportional to their con- 
ductances, i.e. inversely 
proportional to their resist- 
ances.* Thus, if r be a 
wire of 2 ohms resistance 
and r' 3 ohms, then 
current in r: current in 
r' = r' : r = 3 : 2, 
or, f of the whole cur- 
rent will flow through r, and | of the whole current 
through r'. 

The joint resistance of the divided circuit between A 
and B will be less than the resistance of either branch 
singly, because the current has now two paths. In fact, 
the joint conductance will be the sum of the two separate 
conductances. And if we call the joint resistance R, it 
follows that 

1^1 ^ 1 ^ r' +r 
R r r' rr' 

whence R = , or, in words, the joint re- 

r' -\- r 

sistance of a divided conductor is equal to the product of the 
two separate resistances divided hy their sum. This is some- 
times called the laio of shunts, because each of the branches 
may be regarded as a shunt to the other. A simple con- 
struction for finding the value graphically is given in Fig. 
209. Let lines representing the two resistances r and r' 
be erected at the ends of any base line, and the diagonals 

* There is a popular follacj^ that an electric current " alwaj-s takes the 
line of least resistance." It never does, though part of the current may 
flow that way. It divides between the various paths in proportion to their 
easiness. It is only spark discharges which pierce a non-conductor that 
can be said to take the hne of least resistance. 



CHAP. VI RESISTANCES IN PARALLEL 



411 



drawn as shown. The perpendicular at the point of their 
intersection will be the joint resistance R. 

In case there are three or more branches all in parallel, 
as in Fig. 210, the rule may be generalized as follows : — 




Fig. 209. 



Fi?. 210. 



The joint resistance of any number of conductors in parallel 
is the reciprocal of the sum of the reciprocals of the separate 
resistances. 

Kirchhoff has given the following important laws, both 
of them deducible from Ohm's law. 

(i.) In any branching network of wires the algebraic sum 
of the currents in all the loires that meet in any 
point is zero. 

(ii.) When there are several electromotiveforces acting at 
different points of a circuit, the total electromotive- 
force round the circuit is equal to the sum of the 
resistances of its separate parts multiplied, each into 
the strength of the current that flows through it. 

410. Current Sheets. — When a current enters a solid 
conductor it no longer flows in one line but spreads 
out and flows through the mass of the conductor. When 
a current is led into a thin plate of conducting matter it 
spreads out into a current sheet and flows through the plate 
hj stream-lines in directions that depend upon the form of 
the plate and the position of the pole by which it returns 
to the battery. Thus, if wires from the two poles of a 
battery are brought into contact with two neighbouring 



412 ELECTRICITY AND MAGNETISM part ii 

points A and B in the middle of a very large flat sheet 
of tinfoil, the current flows through the foil not in one 
straight line from A to B, but in stream-lines, which start 
out in all directions from A, and curl round to meet in 
B, in curves very like those of the "lines of force" that 
run from the N pole to the S pole of a magnet (Fig. 67). 
When the earth is used as a return wire to conduct the 
telegraph currents (Fig. 274), a similar spreading of the 
currents into current sheets occurs. 



Lesson XXXIY. — Electrical Measurements 

411. Measurement of Resistance. — The practical elec- 
trician has to measure electrical resistances, electromotive- 
forces, and the capacities of condensers. Each of these 
several quantities is measured by comparison with ascer- 
tained standards, the particular methods of comparison 
varying, however, to meet the circumstances of the case. 
Only a few simple cases can be here explained. 

Ohm's law shows us that the strength of a current due 
to an electromotive-force falls off in proportion as the 
resistance in the circuit increases. 

(a) Method of Substitution. — It is therefore possible to 
compare two resistances with one another by finding out 
in what proportion each of them will cause the current of 
a constant battery to fall off. Thus, suppose in Fig. 207 
we have a standard battery of a few Daniell's cells, 
joined up in circuit with a wire of an unknown resistance 
R, and with a galvanometer, we shall obtain a current of 
a certain strength, as indicated by the galvanometer needle 
experiencing a certain deflexion. If we remove the wire 
R, and substitute in its place in the circuit wires whose 
resistances we know, we may, by trying, find one which, 
when interposed in the path of the current, gives the same 
deflexion on the galvanometer. This wire and the one 
we called R offer equal resistance to the current. This 



CHAP. Ti MEASUREMENT OF RESISTANCE 413 

method of substitution of equivalent resistances was further 
developed by Wheatstone, Jacobi, and others, when they 
proposed to employ as a standard resistance a long thin 
wire coiled upon a wooden cylinder, so that any desired 
length of the standard wire might be thrown into the 
circuit by unwinding the proper number of turns of wire 
off the cylinder, or by making contact at some point at 
any desired distance from the end of the wii'e. This form 
of rheostat was found, however, to be less accurate than 
the resistance coils described below. 

(F) Method of Proportional Deflexion. — The method 
explained above can be used with any galvanometer of 
sufficient sensitiveness, but if a tangent galvanometer is 
available the process may be shortened by calculation. 
Suppose the galvanometer and an unknown resistance R 
to be included in the circuit, as in Fig. 207, and that the 
current is strong enough to produce a deflexion S : ]^ow 
substitute for R any known resistance R', which will alter 
the deflexion to 8'; then (provided the other resistances of 
the circuit be negligibly small) it is clear that since the 
strengths of the currents are proportional to tan S and 
tan 8' respectively, the resistance R can be calculated by 
the inverse proportion. 

tan 8 : tan 8' = R' : R. 

(c) Method of Differential Galvanometer. — With a dif- 
ferential galvanometer (Art. 217), and a set of standard 
resistance coils, it is easy to measure the resistance of a 
conductor. Let the circuit divide into two branches, as 
in Fig. 211, so that- part of the current flows through the 
unknown resistance and round one set of coils of the 
galvanometer, the other part of the current being made to 
flow through the known resistances and then round the 
other set of coils in the opposing direction. When we 
have succeeded in matching the unknown resistance by 
one equal to it from amongst the known resistances, the 
currents in the two branches will be equal, and the needle 



414 ELECTRICITY AND MAGNETISM part ii 

of the differential galvanometer will show no deflexion. 
This null method is very reliable. 

{d) Bridge Method. — The best of all the ways of 
measuring resistances is, however, with the important 
instrument known as Wheatstone's Bridge, described 
below in Art. 413. 

(e) Condenser Methods. — To measure very high resist- 
ances the plan may be adopted of charging a condenser 
from a standard battery for a definite 
J^-iff.^ time through the resistance, and then 
GcdvV ascertaining the accumulated charge 
by discharging it through a ballistic 
galvanometer (Art. 218). Or in an- 
other method the condenser is allowed 
to discharge itself slowly through the 
high resistance, and the time taken 
by the potential to fall through any 
given fraction of its original value is 
observed. This time is proportional 
to the resistance, to the capacity, and to the logarithm of 
the given fraction. 

412. Fall of Potential along a Wire. — To under- 
stand the principle of Wheatstone's Bridge we must ex- 
plain a preliminary point. If the electric potential of 
different points of a cii'cuit be examined by means of an 
electrometer, as explained in Art. 289, it is found to 
decrease all the way round the circuit from the + pole of 
the battery, where it is highest, down to the —pole, where 
it is lowest. If the circuit consist of one wire of uniform 
thickness, which offers, consequently, a uniform resistance 
to the current, it is found that the potential falls uni- 
formly ; if, however, part of the circuit resists more than 
another, it is found that the potential falls most rapidly 
along the conductor of greatest resistance. If with a suit- 
able voltmeter we explore the fall of potential between two 
points a and 6 of a circuit (Fig. 212), we shall find in every 
case the fall of potential proportional to the resistance 




FALL OF POTENTIAL 415 




between those two points. For Y = CR, and therefore, for 
the same C, the Y across any part is proportional to the 
E of that part. We know, for example, that when we 
have gone round the circuit to a point where the potential 
has fallen through half its value, the current has at that 
point gone through half the 
resistances. The best way to 
measure a very large current 
is to measure (with sensitive 
voltmeter arrangement of gal- 
vanometer) the drop of poten- 
tial it produces when sent ^ 212. 
through a known very low 
resistance such as a strip of platinoid having exactly 
Y^g-Q ohm resistance between two measured points. 
To measure a very small resistance, it should be put in 
series with another known very small resistance, and 
the drops of potential when the same current flows 
through both are compared : the resistance of each being 
as the drop in potential between its ends. 

413. Wheatstone's Bridge. — This instrument, in- 
vented by Christie, and applied by Wheatstone to meas- 
ure resistances, consists of a system of conductors shown 
in diagram in Fig. 213. This circuit of a battery is made 
to branch at P into two parts, which reunite at Q, so 
that part of the current flows through the point M, the 
other part through the point N. The four conductors 
D, C, B, A, are spoken of as the " arms " of the " balance '' 
or " bridge " ; it is by the proportion subsisting between 
their resistances that the resistance of one of them can be 
calculated when the resistances of the other three are 
known. When the current which starts from C at the 
battery arrives at P, the potential will have fallen to a 
certain value. The potential of the current in the upper 
branch again falls to M, and continues to fall to Q. The 
potential of the lower branch falls to N, and again falls 
till it reaches the value at Q. Now if N be the same 



416 



ELECTRICITY AND MAGNETISM part ii 



proportionate distance along the resistances between P 
and Q, as M is along the resistances of the upper line 
between P and Q, the potential will have fallen at N to 
the same value as it has fallen to at M ; or, in other 
words, if the ratio of the resistance C to the resistance D 




Fig, 213. 

be equal to the ratio between the resistance A and the 
resistance B, then M and N will be at equal potentials. 
To find out whether they are at equal potentials a sensi- 
tive galvanometer is placed in a branch wire between M 
and N; it will show no deflexion when M and JST are at 
equal potentials ; or when the four resistances of the arms 
" balance " one another by being in proportion, thus : — 

A:C::B:D. 

If, then, we know what A, B, and C are, we can calculate 
D, which will be 

p_ B X C 



Example. — Thns if A and C are (as in Fig. 216) 10 ohms 
and 100 ohms respectively, and B be 15 ohms, D will be 
15 X 100 ^ 10 = 150 ohms. 



RESISTANCE COILS 



417 



414. Resistance Coils. — Wires of standard resist- 
ance are now sold by instrament-makers under tlie 
name of Resistance Coils. They consist of coils of some 
alloy, German-silver, platinum-silver, or platinoid (see 
Art. 404), wound AYith 
great care, and adjusted 
to such a length as to 
have resistances of a de- 
finite number of ohms. 
In order to avoid self- 
induction, and the con- 
sequent sparks (see Art. 
458) at the opening or 
closing of the circuit, 
they are wound in the peculiar non-inductive manner 
indicated in Fig. 214, each wire (covered with silk or 
paraffined-cotton) being doubled on itself before being 
coiled up. Each end of a coil is soldered to a solid brass 




Fi-. 214. 




piece, as coil 1 to A and B, coil 2 to B and C ; the brass 
pieces being themselves fixed to a block of ebonite (form- 
ing the top of the "resistance-box"), with sufficient room 
between them to admit of the insertion of stout well- 
fitting plugs of brass. Fig. 215 shews a complete resist- 
ance-box, as fitted up for electrical testing, with the plugs 
in their places. So long as the plugs remain in, the 
2e 



418 



ELECTRICITY AXD MAGNETISM part ii 



cm-rent flows tlu"oiigh the solid brass pieces and plugs 
without encountering any serious resistance ; but when 
any plug is removed, the current can only pass from the 
one brass piece to the other by traversing the coil thus 
thrown into circuit. The series of coils chosen is usually 
of the following numbers of ohms' resistance — 1, 2^ 
2, 5; 10, 20, 20, 50; 100, 200, 200, 500; ... up to 
10,000 ohms. By pulling out one plug' any one of these 
can be thrown into the cu'cuit. and antr desired, whole 




Fig. 216. 



number, up to 20,000, can be made up by pulling out 
more plugs ; thus a resistance of 263 ohms will be made 
up as 200 + 50 + 10 + 2 + 1 by unpkigging those five 
coils. 

It is usual to construct "Wheatstone's bridges with some 
balancing resistance coils in the arms A and C, as well as 
with a complete set in the arm B. The advantage of this 
arrangement is that by adjusting A and C we determine 
the proportionality between B and D, and can, in certain 
cases, measure to fractions of an ohn- Fig. 216 shows a 



CHAP. VI KESISTAKCE BRIDGES 419 

Diore complete scheme, in which resistances of 10, 100, 
and 1000 ohms are included in the arms A and C. 

Example. — Suppose we bad a wire, whose resistance we 
knew to be between i6 and 47 obnis, and wished to 
measure the fraction of an ohm, we should insert it at D, 
and make A 100 ohms and C 10 ohms ; in that case D 
would be balanced by a resistance in B 10 times as great 
as the wire D. If, on trial, this be found to be 464 ohms, 
we know that D = 4G4 X 10 ^ 100 = 46-4 ohms. 

415. Other Patterns of Bridge. — In practice the 
bridge is seldom or never made in the lozenge-shape of 
the diagrams. 

Post-Office Bridge. — The resistance-box of Fig. 215 is, 
in itself, a complete "bridge" of the post-office pattern, 
the appropriate connexions being made by screws at 
various points. In using the bridge the battery circuit 
should always be completed by depressing the key K^ 
before the key K2 o^ the galvanometer circuit is depressed, 
in order to avoid the sudden violent " throw " of the 
galvanometer needle, which occurs on closing circuit in 
consequence of seK-induction (Art. 458). 

Dial Bridge. — To avoid errors arising from the differ- 
ent numbers of plugs in use, the coils of a bridge are 
sometimes arranged in dials — the units in one, the tens 
of ohms in another, and so forth — each dial having but 
one plug, or a movable arm like Fig. 206. 

Metre Bridge. — This is a simple form very useful for 
measuring resistances not exceeding a few hundred ohms. 
Upon a long board is stretched over a scale one metre 
long a uniform thin wire of German-silver or other alloy, 
its ends being joined to stout pieces of copper. A, B, C, 
and D are four resistances joined as shown by stout strips 
of copper. When the wire from the galvanometer is slid 
along the Avire to such a point that there is no current, it 
follows that 

A + a:B + & = C:D. 



420 



ELECTRICITY AND MAGNETISM part ii 



Foster's method of measuring small differences of resist- 
ance is to get balance at a certain point along the wire, 
then interchange A and B, and again get balance at 
another point. The resistance of the piece of wire be- 



A /""C "'^ D ^ B 



Fig. 21T. 

tween the two points will then be equal to the difference 
of the resistances A and B. 

In a simpler way of using the bridge, A and B are 
replaced by strips of no appreciable resistance, so that 

a:&::C:D. 

If D is the u.nknown resistance and C a known resist- 
ance, the ratio of the lengths a and h at once enables the 
unknown resistance to be calculated. 

For further details of bridge methods consult Gray's 
Absolute Measurements in Electricity and Magnetism, 
Kempe's Electrical Measurement, or Ayrton's 
Practical Electricity. 

416. Measurement of Electromotive-Force. — There 
being no easy absolute method of measuring electromo- 
tive-forces, they are usually measured relatively, by com- 
parison with the electromotive-force of a standard cell, 
such as Clark's (Art. 188) , The methods of comparison 
are various; only five are here mentioned. 

(a) Reduced Befiexion Method. — Call E the electro- 
motive-force of the battery to be measured, and E' that of 
a standard battery. Join E with a galvanometer, and let 
it produce a deflexion of \ degrees through the resist- 



I 



CHAP. TI 



POTENTIOMETER. 



421 



ances of the cii'cuit ; then add enough resistance r to 
bring down the deflexion to h., degrees — say 10 degrees 
less than before. jS'ow substitute the standard battery in 
the circuit and adjust the resistances till the deflexion is 
8j as before, and then add enough resistance r' to bring 
down the deflexion to S^- Then 

r' : r = E' : E, 

since the resistances that will reduce the strength of the 
current equally will be proportional to the electromotive- 
forces. (Not recommended.) 

(6) Potentiometer Method. — If the poles of a standard 
battery are joined by a long thin w^ire, the potential will 
fall uniformly from the + to the — pole. Hence, by 




Ym. 218. 



making contacts at one pole and at a point any desired 
distance along the wire, any desu*ed proportional part of 
the whole electromotive-force can be taken. This pro- 
portional part maybe balanced against the electromotive- 
force of any other battery as follows : — Let a uniform 
thin wire of platinoid or German-silver be stretched over 
a scale divided into say 2000 parts. Connect a Clark 
standard cell C through a sensitive galvanometer, as 
shown in Fig. 218, to make contact at the 1434 division 
of the scale. Then connect a single accumulator cell 
B, or two Daniell's, or a Grove cell with a sliding 
contact, and move it up and down until a point is found 



422 ELECTRICITY AND MAGNETISM part ii 

such that the galvanometer shows that the Clark cell 
is balanced. Then connect the cell X whose E.M.F. is 
to be measured, and slide its contact along the wire 
until it also is balanced. Suppose it balances at 1024 
of the scale, its E.M.F. will be 1-024. A single galvan- 
ometer will suffice if the wire to X is joined in between 
G and the Clark cell. 

(c) Voltmeter Method. — If a galvanometer be con- 
structed so that the resistance of its coils is several 
thousand ohms (in comparison with which the internal 
resistance of a battery or dynamo machine is insignifi- 
cant), it will serve to measure electromotive-forces; for 
the strength of current through it will depend only on 
the electromotive-force between the ends of the coil. 
(See Art. 220 on Voltmeters.) 

(d) Condenser Method. — A condenser of known 
capacity is charged from a standard cell, and then dis- 
charged through a ballistic galvanometer (Art. 218). 
The cell to be compared is then substituted for the 
standard cell. The E.M.F. is proportional to the throw 
of the galvanometer. 

(e) Electrometer Method, — The electromotive-force 
of a battery may be measured directly as a difference of 
potentials by a quadrant electrometer. In this case the 
circuit is never closed, and no current flows. 

417. Measurement of Internal Resistance of Cells. — 
This may be done in several ways. 

(a) Condenser Method. — As in (c?) of preceding 
Article, observe throw of galvanometer from condenser 
charged by the cell. Then shunt the cell with a suitably 
high resistance K, and take another charge and discharge. 
If the two throws are called d^ and r/o, the internal resist- 
ance will be = R(c7j — d.2)/d.2. 

(b) Half-dejlexion Method. — Place the cell in series 
with a galvanometer the resistance of which is G, and a 
resistance-box in which there is unplugged a resistance R 
such that the deflexion is conveniently large. Xow in- 



CHAP. VI ^fETHODS OF MEASUREMENT 423 

crease the resistance in the box until it is seen by the 
deflexion that the current has been reduced to half 
what it was. If this added resistance is called a, then 
by Ohm's law it follows that the internal resistance is 
= a — (R + G). This method is suitable for very high 
internal resistances. 

(c) Method of Opposition. — Take two similar cells 
and join them in opposition to one another, so that they 
send no current of their own. Then measure their 
united resistance just as the resistance of a wire is 
measured. The resistance of one cell will be half that 
of the two. 

(^) Mances Method. — Place the cell itself in one 
arm of the Wheatstone's bridge, and put a key where 
the battery usually is, adjust the resistances till the 
permanent galvanometer deflexion is the same whether 
the key be depressed or not. When this condition 
of things is attained the battery resistance is balanced 
by those of the other three arms. {Not a reliable 
method.') 

(e) Alternate Current Method. — If greater accuracy is 
required in the opposition method, the cells in opposition 
may be placed in one of the arms of a Wheatstone's bridge 
in which instead of the usual battery is inserted the sec- 
ondary coil of a small induction coil (without condenser), 
and with which a telephone receiver is used instead 
of a galvanometer. The ceasing of the buzzing in the 
telephone corresponds to nul deflexion. By this means 
we avoid the disturbance of the balance of the opposing 
cells which occurs if continuous cm-rents are used. This 
method is also excellent for measuring resistances of 
liquids. 

418. Measurement of Capacity. — The capacity of a 
condenser may be measured by comparing it with the 
capacity of a standard condenser — such as the \ micro- 
farad condenser (Fig. 159) — in one of the following 
ways : — 



424 ELECTRICITY AND MAGNETISM paht ii 

(a) Electrometer Method. — Charge the condenser of 
unknown capacity to a certain potential; then make it 
share its charge with the condenser of known capacity, 
and measure the potential to which the charge sinks; 
then calculate the original capacity, which will bear the 
same ratio to the joint capacity of the two as the final 
potential bears to the original potential. 

(b) Ballistic Galvanometer Method. — Charge each con- 
denser to equal differences of potential from the same cell 
or battery, and then discharge each successively through 
a ballistic galvanometer (Art. 188). The throw of the 
needle w^ill be proportional in each case to the charge, 
and therefore to the capacity. 

The law of the ballistic galvanometer is : — 
KV=Q = — — -sin^a, 

G 77 

where Q is the quantity of electricity (in C.G.S. units), H the 
magnetic field, by the constant of the galvanometer, T the 
period of one complete swing of the needle, and o. the angle 
of first swing. The factor H/G may be eliminated by passing a 
steady current C to produce a steady deflexion /3 ; when 

C = ?tan)3. 
G 

Combining this with the preceding, we have 

CT sin I g 
^~ 77 tan ^ 

If a and /3 are both small this becomes 

Q = CT a/2 rr^. 

If C is in amperes, Q will be in coulombs. 

(c) Bridge Method. — Connect the two condensers Kj 
and Kg in two arms of a Wheatstone's bridge and adjust 



CHAP. VI MEASUREMENT OF CAPACITY 



425 



the resistances so that tliere is no deflexion on charge or 
discharge (Fig. 219). Then K^-.K^- • r^'-r^, the laj-ger 
capacity acting as a smaller resistance. 

(d) Potential-divider nul Method. — Two resistances r^ 
and r., are joined in series to the + and — poles of a 
battery. Tlie middle point between r^ and r^ is connected 
to one of the terminals of Kj and also of Ka* The free 




iiM 

Fig. 219. 

terminals of Kj and Kg are momentarily joined to the + 
and — poles of the battery respectively and receive charges 
of opposite sign. They are then connected; and if of 
equal amount the charges will neutralize each other. The 
resistances r^ and ?'2 are adjusted until this condition is 
satisfied, as shown by nul deflexion when the key of a 
galvanometer circuit across their terminals is depressed. 
Then K^ '.ls.^::r^: ry 

(e) Tuning-fork Method. — A tuning-fork acting as a 
\dbrating two-way switch charges and discharges the con- 
denser n times per second, allowing to pass \Kn coulombs 
per second or VKn amperes. The apparent resistance r 
of this combination is 1/Kn, and can be measured by a 
Wheatstone bridge, whence K = 1/nr. 

(/) Loss of Charge Method. — This is the same as the 
last method in Art. 41 le, a known high resistance being 
used. 



CHAPTER VII 

THERMO-ELECTRICITY 

Lessox XXXV. — Thermo-Eleclric Currents 

419. Seebeck Effect. — In 1822 Seebeck discovered 
that a current may be produced in a closed circuit by 
heating a point of contact of two dissimilar metals. If 
a piece of bismuth and a piece of antimony be soldered 
together, and their free ends connected with a short-coil 
galvanometer, it is found that if the junction be warmed 
to a temperature higher than that of the rest of the cir- 
cuit, a current flows in the direction from bismuth to 
antimony across the heated point; the current being pro- 
portional to the excess of temperature. If the junction 
is cooled below the temperature of the rest of the circuit 
a current in the opposite direction is observed. The 
electromotive-force thus set up will maintain the current 
so long as the excess of temperature of the heated point 
is kept up ; heat being all the while absorbed in order to 
maintain the energy of the current. Such currents are 
called Thermo-electric currents, and the electromotive- 
force producing them is known as Thermo-electromotive- 
force. 

420. Peltier Effect. — In 1831 Peltier discovered 
a phenomenon which is the converse of that discovered 
by Seebeck. He found that if a current of electricity 
from a battery be passed through a junction of dissimilar 

426 



CHAP, rii THER:\rO-ELECTRIC EFFECTS 427 

metals the junction is either heated or cooled, according 
to the direction of the current. Thus a current which 
passes through a bismuth-antimony pair in the direction 
from bismuth to antimony absorbs heat in passing the 
junction of these metals, and cools it ; whereas, if the 
current flow from antimony to bismuth across the junc- 
tion it evolves heat, and the junction rises in tempera- 
ture. It is clear that if bismuth is positive with respect 
to antimony, any current that may be caused to flow 
from bismuth to antimony is aided by the electromotive- 
force at that junction; whilst any current flowing from 
antimony to bismuth will meet with an opposing electro- 
motive-force. In the latter case the current wdll do work 



Fig. 220. 

and heat the junction ; in the former the current will 
receive energy at the expense of the junction, which wdll 
give up heat. In Fig. 220, the feathered arrows at the 
junctions represent the Peltier electromotive-forces, and 
the plain arrows the direction of the current. 

This phenomenon of heating (or cooling) by a current, 
where it crosses the junction of tw^o dissimilar metals 
(known as the "Peltier effect," to distinguish it from the 
ordinary heating of a cii'cuit where it offers a resistance 
to the current, which is sometimes called the " Joule 
effect "), is utterly different from the evolution of heat 
in a conductor of high resistance, for (a) the Peltier effect 
is reversible ; the current heating or cooling the junction 
according to its direction, whereas a current meeting with 
resistance in a thin wire heats it in whichever direction 
it flows ; and (h) the amount of heat evolved or absorbed 
in the Peltier effect is proportional simply to the current, 
not to the square of the current as the heat of resist- 
ance is. 



428 



ELECTRICITY AND MAGNETISM part ii 



The complete law of the heat developed in a ckcuit 
will therefore require to take into account any Peltier 
effects which may exist at metal junctions in the circuit. 
If the letter P stand for the difference of potential due 
to the heating of the junction, expressed as a fraction of 
a volt, then the complete law of heat is 



U=:0-24x (C2R«±PC0, 



which the student should compare with Joule's law in 
Art. 427. The quantity called P is also known as the 
coefficient of the Peltier effect ; it has different values for 
different pairs of metals, and is numerically equal to the 
number of ergs of work which are evolved as heat at a 
junction of the particular metals by the passage of one 
absolute unit (10 coulomhs) of electricity through the 
junction. 

421. Thermo-electric Laws. — The thermo-electric 
properties of a circuit are best studied by reference to 

the simple circuit 
of Fig. 221, which 
represents a bis- 
muth - antimony 
pair united by a 
copper wire. If 
all parts of the 
circuit are at one 
temperature, even 
though there may 
be at the junc- 
tions electromo- 
tive-forces as suggested above, there will be no current, 
since the electromotive-forces are in equilibrium. But 
when a junction is heated this equilibrium no longer 
exists, and there will be a resultant electromotive-force. 
It is found to obey the following laws : — 




Fifr. 221. 



CHAP. TIT THERMO-ELECTRIC POWER 429 

(i.) TTie thermo-elect?'omoiive-force is, for the same pair 
of metals, proportional (through limited ranges of 
temperature) to the excess of temperature of the 
junction over the rest of the circuit. 
(ii.) The total theniio-electromotive-force in a circuit is the 
algebraic sum of all the separate thermo-electromotive- 
forces in the various parts. 
It follows from this law that the various metals can be 
arranged, as Seebeck found, in a series, according to their 
thermo-electric power, each one in the series being thermo- 
electrically positive (as bismuth is to antimony) toward 
one lower down. 

422 . Thermo-electric Power. — In the following table 
is shown the thermo-electric series of metals, together with 
the thermo-electric power of each when cold. The term 
thermo-electric power of a metal means the electromotive- 
force per degree (centig.) for a pair made of that metal 
with the standard metal (lead). In the table the numbers 
are microvolts per degree. 



-f Bismuth . 

Nickel 

German-silver 

Lead . 

Platinum . 

Copper 

Zinc . 

Iron . 
— Antimony . 

Tellurium . 

Selenium . 



89 to 97 
22 

11-75 


- 0-9 

- 1-36 

- 2-3 
-17-5 

-22-6 to -26-4 
502 
800 



A very small amount of impurity may make a great 
difference in the thermo-electric power of a metal, and 
some alloys, and some of the metallic sulphides, as galena, 
exhibit extreme thermo-electric piower. 

The electromotive-forces due to heating single pairs 
of metals are very small indeed. If the junction of a 
copper-iron pair be raised 1° C. above the rest of the 
circuit its electromotive-force is only 15T4: microvolts. 



430 ELECTRICITY AND MAGNETISM part ii 

That of the more powerful bisiimth-autimony pair is 
for l'^ C, about 117 microvolts. Thermo-electric power 
varies, however, with teuiperatui-e : for example, that of 
iron is really — 17-5 + 0-01:9^ (where t is the mean tem- 
perature of the two junctions), iron becoming less nega- 
tive when hot. Copper is — 1-36 — 0-01?, becoming more 
negative. There will be obviously one particular tem- 
perature or neutral point, at which their powers will be 
equal. 

423. Thermo-electric Inversion. — Cummiug discov- 
ered that in the case of iron and other metals an 
inversion of their thermo-electric properties may take 
place at a high temperature. In the case of the copper- 
iron pair the temperature of 275° is a neutral point; 
below that temperature the current flows through the 
hotter junction from the copper to the iron ; but when 
the circuit is above that temperature iron is thermo- 
electrically positive to copper. The neutral point for a 
zinc-iron pair is about 200°. The inversion is easily 
shown by heating the junction of two long strips of these 

metals, riveted . together in a 
Y-form, and watching the effect 
on a galvanometer connected to 
their other ends. There will 
at first be a deflexion which 
will go on increasing until the 
temperature of 200° is attained, 
but on further heating the junc- 
.00-' .00" 300' 400^ c tion the deflexion diminishes and 
°' " ' at about 400° reverses, the cur- 

rent flowing the other way. Fig. 222 shows graphically 
the curves obtained with iron-zinc and iron-copper pairs 
when one junction is kept at 0° while the other is heated. 
The dotted line is for the iron-zinc pair when one junction 
is kept at 50° and the other heated. 

424. Thermo-electric Diagram. — The facts of 
thermo-electricity are best studied by means of the 




CHAP. VII THERMO-ELECTRIC DIAGRAM 



431 



diagrams suggested by Lord Kelvin and constructed by 
Professor Tait. In that given in Fig. 223 the horizontal 
divisions represent the temperatures ; the vertical dis- 
tances indicating the thermo-electric power, in microvolts 
per degree. These powers are measured with respect to 
the metal lead, which is taken as tlie standard of zero at 
all temperatures, because, Avhile with other metals there 



V 
+5 



LEIAD 



-5 



.Cp.p., 



-10 



■1- 



-15 



0° 



100 



JOO 



300 



400 



500 



Fig. 223. 



appears to be a' difference of potentials between the metal 
hot and the same metal cold, hot lead brought into contact 
with cold lead shows no perceptible thermo-electric differ- 
ence. 

An example will illustrate the usefulness of the dia- 
gram. Let a circuit be made by uniting at both ends a 
piece of iron and a piece of copper; and let the two 
junctions be kept at 0° and 100° respectively by melting 
ice and boiling water. Then the total electromotive-force 
round the circuit is represented by the area a, 0, — 15, b. 



432 ELECTRICITY AND MAGNETISM part ii 

The slope of the lines for the various metals represents 
the property referred to above, of an electromotive-force 
between differently-heated portions of the same metal 
accompanied by an absorption or evolution of heat when 
the current flows from a hotter to a colder portion of the 
same metal. This effect, known as the Thomson e#ect 
from its discoverer Sir W. Thomson (Lord Kelvin), is 
opposite in iron to v^hat it is in copper or zinc. Copper 
when hot is negative compared with copper that is cold. 
Hence if a current is sent from a hot to a cold part of a 
piece of copper it encounters an opposing electromotive- 
force. Hence when a current of electricity flows from a 
hot to a cold point in copper it evolves heat ; and it 
absorbs heat when it flows from a cold point to a hot 
point in the copper. In iron a current flowing from a 
hot point to a cold point absorbs heat. 

The thermo-electromotive-force of a pair, of which 
the junctions are at temperatures T and t respectively, 
and of which n is the temperature of the neutral point, 
may be conveniently expressed by the following formula: — 

where p is the volts per degree (at 0°) as given in the 
table (Art. 422). 

425. Thermo-electric Piles. — The electromotive- 
force of a bismuth-antimony pair, when the junctions are 
kept at 0° and 100°, is only 0-0115 volt. In order to 
increase the electromotive-force of thermo-electric pairs 
it is usual to join a number of pairs of metals (preferably 
bismuth and antimony) in series, but so bent that the 
alternate junctions can be heated as shown in Fig. 224 at 
BBB, whilst the other set AAA are kept cool. The 
various electromotive-forces then all act in the same 
direction, and the current is increased in proportion to 
the number of pairs of junctions. Powerful thermo- 
electric batteries have been made by Clamond — an iron- 



CHAP. VII 



THERMOPILES 



433 



galena battery of 120 pairs affording a strong current ; 
but it is extremely difficult to maintain them in effective 
action for long, as they fail after continued use, probably 
owing to a permanent molecular change at the junctions. 
In the hands of Melloni the thermo-electric pile or ther- 
mopile, constructed of many small pairs of antimony 
and bismuth united in a compact form, proved an ex- 
cellent electrical thermometer w^hen used in conjunction 
with a sensitive short-coil astatic galvanometer. For the 




Fig-. 224. 



detection of excessively small differences of temperature 
the thermopile is an invaluable instrument, the currents 
being proportional to the difference of temperature 
between the hotter set of junctions on one face of the 
thermopile and the cooler set on the other face. Tlie 
arrangement of a thermopile with the old astatic galvan- 
ometer is shown in Fig. 225. 

A still more sensitive arrangement for detecting 
minute heating due to radiation consists in suspending 
between the poles of a powerful magnet a closed circuit 
having a bismuth-antimony junction in it. Sturgeon 



434 



ELECTRICITY AND MAGNETISM part ii 



proposed a thermo - galvanometer on this plan in 
1835. 

In the radio-micrometer of Yernon Boys (1889) a loop 
of wire, suspended by a delicate quartz fibre betwg^n the 




poles of a magnet (like the coil in Fig. 126) has its circuit 
closed at its lower end by a piece of antimony and a 
piece of bismuth (or alloys of these metals) soldered to a 
minute disk of copper foil. A rise of temperature of the 
copper foil even so small as one millionth of a degree will 
generate a current in the loop and give a deflexion over 
one division of the scale. With an instrument of this 
kind the radiant heat of a candle can be detected at a 
distance of two miles. 



CHAPTER YIII 

HEAT, POWER, AND LIGHT, FROM ELECTRIC CURRENTS 

Lessox XXXYI. — Heating Effects of Currents 

426. Heat and Resistance. — A current may do 
work of various kinds, chemical, magnetic, mechanical, 
and thermal. In every case where a current does work 
that work is done by the expenditiu-e of part of the 
energy of the current. We have seen that, by the law of 
Ohm, the current produced by a given battery is dimin- 
ished in strength by anything that increases the external 
resistance. But the current may be diminished, in 
certain cases, by another cause, namely, the setting up 
of an opposing electromotive-force at some point of the 
circuit. Thus, in passing a current through an electro- 
lytic cell (Art. 237) there is a diminution due to the 
opposing electromotive-force (" polarization ") which is 
generated while the chemical work is being done. So, 
again, when a current is used to drive an electric motor 
(Art. 443), the rotation of the motor will itself generate 
a back E.M.F., which will diminish the current. What- 
ever current is, however, not expended in this way in 
external work is frittered down into heat, either in the 
battery or in some part of the circuit, or in both. Suppose 
a quantity of electricity to be set flowing round a closed 
circuit. If there were no resistance to stop it it would 
circulate for ever ; just as a waggon set rolling along a 
435 



436 



ELECTRICITY AND MAGNETISM part n 



circular railway should go round for ever if it were not 
stopped by friction. When matter in motion is stopped 
by friction the energy of its motion is frittered down by 
the friction into heat. When electricity in motion is 
stopped by resistance the energy of its flow is frittered 
down by the resistance into heat. Heat, in fact, appears 
wherever the circuit offers a resistance to the current. 
If the terminals of a battery be joined by a short thick 
wire of small resistance, most of the heat will be de- 
veloped in the battery and so wasted ; whereas,, if a thin 
wire of relatively considerable resistance be interposed in 
the outer circuit, it will grow hot, while the battery itseK 
will remain comparatively cool. 

427. Laws of Development of Heat: Joule's Law. — 
To investigate the development of heat by a current, 

Joule and Lenz used in- 
struments on the principle 
shown in Fig. 226. A 
thin wire joined to two 
stout conductors is en- 
closed within a glass vessel 
containing alcohol, into 
which also a thermometer 
dips. The resistance of 
the wdre being known, its 
relation to the other resist- 
ances can be calculated. 
Joule found that the num- 
ber of units of heat developed 
in a conductor is proportional — 
(i.) to its resistance ; 
(ii.) to the square of the strength of the current ; 

and 
(iii.) to the time that the current lasts. 
The equation expressing these relations is known as 
Joule's Law, and is — 

U = C2R« X 0-24, 




CHAP. VIII JOULE'S LAW 437 

where C is the current in amperes, R the resistance in 
ohms, t the time in seconds, and U the heat in calories ; 
one calorie being the amount of heat that will raise 
1 gramme of water through 1° C. of temperature 
(Art. 281). 

This equation is equivalent to the statement that a 
current of one ampere fioioing through a resistance of one 
ohm developes therein 0*24 calories per second. The proof 
of this rule is given in Art. 439. The heat produced 
thus by the degradation of energy in a ]-esistance is 
sometimes called the "ohmic" heat to distinguish it 
from the reversible Peltier effect (Art. 420). 

The electric unit of heat, the Joule, is only 0-24 of an 
ordinary heat-unit or calorie, and 1 calorie will be equal 
to 4-2 joules. 

The second of the above laws, that the heat is, coeteris 
paribus, proportional to the square of the strength of the 
current, often puzzles young students, who expect the 
heat to be proportional to the current simply. Such 
may remember that the consumption of zinc is, cceteris 
paribus, also proportional to the square of the current ; 
for, suppose that in working through a high resistance 
(so as to get all the heat developed outside the battery) 
we double the current by doubling the number of battery 
cells, there will be twice as much zinc consumed as before 
in each cell, and as there are twice as many cells as at 
first the consumption of zinc is four times as great as 
before. 

428, Favre's Experiments. — Favre made a series of most 
important experiments on the relation of the energy of a current 
to the heat it developes. He ascertained that the number of 
calories evolved when 33 grammes (1 equivalent) of zinc are 
dissolved in dilute sulphuric acid (from which it causes hydro- 
gen to be given off) is 18,682. This figure was arrived at by- 
conducting the operation in a vessel placed in a cavity of his 
calorimeter, an instrument resembling a gigantic thermometer 
filled with mercury, the expansion of which was proportional to 
the heat imparted to it. When a Smee's cell was introduced into 



438 ELECTRICITY AND MAGNETISM part ii 



the same instrument, the solution 4i the same amount of zinc 
was observed to be accompanied hj the evolution of 18,674 calo- 
ries {i.e. an amount almost identical with that observed before), 
and this amount was the same whether the evolution took place 
in the battery-cell when the circuit was closed with a short thick 
wire, or whether it took place in a long thin wire placed in the 
external circuit. He then arranged 5 Smee's cells in series, in 
cavities of the calorimeter, and sent their current round a small 
electric motor. The amount of heat evolved during the solution 
of 33 grammes of zinc was then observed in three cases : (i.) when 
the motor was at rest ; (ii.) when the motor was running round 
and doing no work beyond overcoming the friction of its pivots ; 
(iii.) when the motor was employed in doing 13,124,000 gramme- 
centimetres (= 12,874 X 106 ergs) of work, by raising a weight 
hj a cord running over a pulley. The amounts of heat evolved 
in the circuit in the three cases were respectively, 18,667, 18,657, 
and 18,374 calories. In the last case the work done accounts for 
the diminution in the heat wasted in the circuit. If we add the 
heat-equivalent of the work done to the heat evolved in the 
latter case, we ought to get the same value as before. Dividing 
the 12,874 X 10^ ergs of work by Joule's equivalent (42 x 106), 
we get as the heat-equivalent of the work done 306 calories. 
Now 18,374+ 306 = 18,680, a quantity which is almost identical 
With that of the first observation, and quite within the limits of 
unavoidable experimental error. 

429. Rise of Temperature. — The elevation of tem- 
perature ill a resisting wire depends on the nature of the 
resistance. A very short length of a very thin wire may 
resist just as much as a long length of stout wire. Each 
will cause the same number of units of heat to be evolved, 
but in the former case, as the heat is spent in warming a 
short thin wire of small mass, it will get very hot, 
whereas in the latter case it will perhaps onl}" warm to 
an imperceptible degree the mass of the long thick wire, 
which, moreover, has a larger surface to get rid of its 
heat. If the wire weigh to grammes, and have a specific 
capacity for heat .<?, then U = sicO, where 6 is the rise of 
temperature in degrees (Centigrade). Hence if none of 
the heat were radiated away 

e = 0-24 x 9^. 



CHAP. viH RISE OF TEMPERATURE 439 

Since the resistance of metals increases as they rise in 
temperature, a thin wire lieated by the current will resist 
more, and grow hotter and hotter until its rate of loss of 
heat by conduction and radiation into the surrounding air 
equals the rate at which heat is supplied by the current. 

The following pretty experiment illustrates the laws 
of heating. The current from a few cells is sent through 
a chain made of alternate links of silver and platinum 
wires. The platinum links glow red-hot while the silver 
links remain comparatively cool. The explanation is 
that the specific resistance of platinum is about six times 
that of silver, and its capacity for heat about half as 
great ; hence the rise of temperature in wires of equal 
thickness traversed by the same current is roughly twelve 
times as gTeat for platinum as for silver. 

Thin wires heat much more rapidly than thick, the 
rise of temperature in different paints of the same wire 
(carrying the same current) would he, for different thick- 
nesses, inversely proportional to the fourth power of the 
diameters if they had equal surfaces for radiation. 

Thus, suppose a wire at any point to become reduced 
to half its diameter, the cross-section will have an area 
1 as great as in the thicker part. The resistance here 
will be 4 times as great, and the number of heat units 
developed will be 4 times as great as in an equal length 
of the thicker wire. But 4 times the amount of heat 
spent on \ the amount of metal would warm it to a 
degree 16 times as great : and the thin wire has only half 
as much surface for getting rid of heat. But the hotter a 
body becomes the more freely does it radiate heat to 
things around it. For wires of given material, the cunent 
needed to raise them to an equal temperature varies as 
the square root of the cube of the diameter. This law 
applies to the sizes of wires used as safety-fuses in electric 
lighting. These are pieces of tin wire interposed in the 
circuit to melt if by any chance the current becomes abnor- 
mally strong. 



440 



ELECTRICITY AND MAGNETISM part ii 



430. Cardew's Voltmeter. — The current flowing- 
through a long thin wire of platinum when it is made to 
connect two points on a circuit will measure 
the potential difference between these two 
points. Owing to its becoming warmed it 
will expand, and its expansion may be made 
to move a hand over a dial graduated to 
read volts (Fig. 227) . 

431. Electric Cautery. — For surgical pur- 
poses a thin platinum wire, heated red-hot 
by a current, is sometimes used instead of a 
knife, as, for example, in the operation of 
amputating the tongue for cancer. Platinum 
is chosen on account of its infusibility, but 
even platinum wires are fused by the current 
if too strong. Carbon alone, of conductors, 
resists fusion. 

432. Blasting by Electricity. — In con- 
sequence of these heating effects, elec- 
tricity can be applied in blasting and mining 
to ignite the charges. Stout conducting 
wires are carried from an appropriate 
battery at a distance to a special fuze, in 

which a very thin platinum wire is joined in the circuit. 
This wire gets hot w^hen the current flows, and being 
laid amidst an easily combustible substance to serve 
as a priming, ignites this and sets fire to the charge 
of gunpowder. Torpedoes can thus be exploded 
beneath the water, and at any desired distance from 
the battery. 

433. Electric Welding. — If two wires or rods of 
metal are held together with sufiicient force while a very 
large current is passed through them, much heat is 
developed at the junction, so that they soften and become 
welded together. The processes of electric icelding have 
been perfected by Elihu Thomson, who has utilized for 
this purpose alternate-current transformers (Art. 480) to 



Fig. 227. 



CHAP. Till ELECTRIC ENERGY 441 

produce currents of many hundred amperes at a pressure 
of a few volts. 

A singular effect is noticed when two iron rods 
connected to the poles of a powerful source at 50 or 
more volts are dipped into water. The rod which serves 
as kathode is observed to be covered with a luminous 
layer, and it presently becomes red-hot. Guthrie, who 
first investigated this phenomenon in 1876, ascribed the 
heating to the resistance of a film of hydrogen. Recently 
it has been made the basis of a welding method. 

434. Electric Cooking. — Since public supplies of 
electricity became common, electric stoves, ovens, and 
heaters for cooking, stewing, etc., have become articles 
of commerce. The heating is effected by passing cur- 
rents through resistance wires embedded in cement or 
other suitable insulating material. 



Lessox XXXVII. — Electric energy: its Supply and 

Measurement 

435. Electric Energy. — An electric current conveys 
energy from a battery or dynamo to some other part 
of the circuit, where it is transformed back into work, 
— mechanical, chemical, or thermal work. We must 
inquire into this electrical energy, and into the rate 
at which it is generated or transformed. 

Power is the rate at which energy is being received or 
spent. It may be expressed in foot-pounds per second 
or in ergs per second. James Watt considered a horse 
capable on the average of working at the rate of 550 foot- 
pounds per second (against gravity). As 1 foot = 3048 
centimetres, and the force of 1 lb. ( = 453-6 grammes x 981) 
= 445,000 dynes nearly, it follows that 1 horse-power is 
worth 7,460,000,000 (or 746 x 10"^) ergs per second. 

If a quantity of electricity Q is moved through a 
difference of potential V, it follows from the definition 



442 ELECTRICITY AND MAGNETISM part it 

m 

(Art. 263) that the work done is equal to QV. If this 
is occurring in a battery or dynamo, QV represents 
electrically the work (chemical or mechanical) done on 
the system, or the energy received (electrically) by the 
system. Now, suppose this operation to have occupied 
time t, the imte at which the energy is being imparted to 
the circuit will be QJ/t. But (Art. 162) Q/t = C. Hence 
the pmver given to the circuit is equal to CV. 

This justifies the statement that the powe?- of an electric 
current to perform useful work, whether in lighting, 
heating, or producing mechanical actions, is proportional 
both to the strength of the current, and to the electromotive- 
force lohich drives it. In other words, power is pro- 
portional to both amperes and volts jointly. Similarly 
the power of a steam engine is proportional not only to 
the quantity of steam it uses, but also to the pressure at 
which the steam is supplied. The electric unit of power 
will then be the power of a current of 1 ampere driven 
by an electric pressure of 1 volt. This unit is known 
as 1 volt-ampere, or 1 icatt. 

Since 1 volt = lO^ absolute units of E.M.F. (Art. 354) 
and 1 ampere = 10"^ absolute units of current (Art. 354), 
it follows that 1 watt = 10''' absolute units of power {i.e. 
\QP ergs per second). But 1 horse-power = 746 x 10'^ 
ergs per second (see above). Hence 1 H.P. = 746 watts. 

One thousand watts is called 1 Jciloivatt. The kilowatt 
is therefore approximately 1^ H.P. 

To find the number of watts of power supplied by any 
dynamo or battery, multiply the number of amperes of 
current by the number of volts at which the current is 
driven. The same rule serves to calculate the power 
electrically delivered to any motor, lamp, accumulator, 
or other means of spending electric energy. 
Horse-power = C x V -=- 746. 

Example. — If a current of 20 amperes is supplied to a big 
arc-lamp at a pressure of 56 volts, find the amount of 
power absorbed therein. Ans. 1120 ivatts or 1^ H.P. 



CHAP. VIII POWER MEASUREMENTS 443 

436. Intake and Output of Power. — At any gen- 
erator battery, dynamo, or thermopile, power is taken 
in to the electric circuit. At any motor or lamp, or at 
any part in the circuit where chemical work (electro- 
plating, decomposing gases, or charging accumulators) is 
being done or at any place where heat is being evolved, 
power is being given out by the electric circuit. At 
every place where energy is coming in to the circuit 
there will be an electromotive-force in the same direction 
as the current, and helping to drive it. At every part 
where energy is being given out by the circuit there will 
be an electromotive-force in a direction opposed to the 
current.* The word output,^ as applied to dynamos, etc., 
means the number of watts or kilowatts which the 
machine supplies or can supply. For example, a dynamo 
capable of supplying 300 am- 
peres "at "100 volts (meaning 
with an available E.M.F. of 100 
volts) is said to have an output 
of 30 kilowatts. 

437. Power-Measurement. ^ 
— To measure the power given 
electrically to any part ab of 
a circuit by an unvarying cur- ^" ^ 
rent, it suffices to measure the '^^ ^-^ "*"" 
current with an ampere-meter ^^'' " ' 

(Art. 221), and the potenticxls across the part with a 
voltmeter (Arts. 220, 290), the latter being of course con- 

* Consider the mechanical analogue of transmission of power from one 
pulley to another pulley by a belt. The effort in the driving pulley is 
in the same direction as the motion of the belt. The effort in the driven 
pulley is opposed in direction to the motion. (See also Art. 248.) 

This fundamental principle accounts for the back-electromotive-forces 
observed in motors, and in accumulators while being charged. Because 
of it we know (Art. 166) that the seat of the main electromotive-force in a 
voltaic ceU is at the surface of the zinc, and that (Art. 422) bismuth is 
thermo-electrically positive to antimony. 

t The word output, as applied to central station work, is sometimes 
used in sense of total outflow of amperes irrespective of voltage. 



.0 



444 ELECTRICITY AND MAGNETISM part ii 

nected as a shunt as in Fig. 228. The product of volts 
and amperes gives the watts. Or a wattmeter may be 
used as below. 

438. Wattmeters. — The product of amperes and 
volts may be measured directly by means of a wattmeter. 
This name is given to a variety of electrodynamometer 
(Art. 394) in which the fixed and movable coils constitute 
two separate circuits, one being a thick wire of low resist- 

_^ ^ ance to carry the amperes, the 

other being, or including, a 
;Vi;¥iiV'l| thin wire of high resistance (as 

1 ^ in voltmeters) to receive a cur- 

; rent proportional to the volts. 

arc"^ "^ I rr^Tl.., The latter circuit is to be con- 
j ^k~^J nected as a shunt to the part 
1 1 ah of the circuit in which 
^^ ^ J the su^Dplied power is to be 

■' -T ^ "" measured. In Fig. 229, as in 

Fig. 228, the part ah is an arc- 
lamp. The auxiliary resistance r is introduced into the 
thin-wire circuit of the instrument, the whole current 
flowing through the thick-wire circuit. 

Wattmeters are made both on the pattern of Siemens's 
dynamometer (Art. 395) and on that of Kelvin's balances 
(Art. 396). 

AVhen power-measurements have to be made on 
alternate-current circuits, separate instruments must not 
be used, as in Art. 437, to measure volts and amperes. 
For, owing to the differences of phase (Art. 472) between 
voltage and current, the apparent loatts, got by multi- 
plying the separate readings, will be in excess of the true 
watts as measured by a wattmeter. 

439. Power wasted in Heating. — If a current C is 
driven through a resistance R, the volts needed will (by 
Ohm's law) be 

Y^CR. 
The power CY so expended will merely heat the resistance. 



CHAP. VIII DISTRIBUTION OF ELECTRIC ENERGY 445 

Substitute for Y its value as above, and we have 

Watts wasted = CV = C^R = ys/R. 

Or, if the expenditure goes on for t seconds, the amount 
of energy turned into heat (joules) will be 

Energy = QV = QtY = C^R^. 

The nett power of a dynamo or battery is always less 
than its gross power, because of internal resistance. If r 
be the internal resistance, and E the whole electromotive- 
force, the nett or available volts V = E — Cr. The gross 
power will be EC watts. But the nett power will be 
VC = EC — Ch\ Or, the available watts equal the total 
watts generated, less the watts wasted in internal 
heating. 

To prove Joule's law of heating as given in Art. 427, it maybe 
remembered that the mechanical equivalent of heat is 42 million 
ergs to 1 calorie (.Joule's equivalent) , or W = JU, where W is the 
work in ergs, U the heat in calories, and J = 4*2 x 10^ Hence 
U = C^R^/J. But to reduce the work to ergs we must multiply 
C2Rf by W ; whence U = C^Ri X 0-24. 

440. Distribution of Electric Energy. — Electric en- 
ergy is now" distributed on a large scale for lighting, 
motive power and heating. Large Central Stations or 
Power-houses are erected at convenient spots, with steam- 
engines or turbines (if water-power is available) to drive 
generating machinery (dynamos and alternators). From 
the power-house distributing mains of copper go out, con- 
sisting of feeders leading into the netiuork of couductors 
that runs from house to house. 

Supply systems may be classified according to whether 
they operate at a low voltage (or low pressure), i.e. from 
100 volts (or under) to 300 volts ; high voltage, i.e. from 
300 to 3000 volts ; or extra high voltage, over 3000 
volts. The low-voltage systems generally use continuous 
currents, the high-voltage systems generally (but not 
necessarily) use alternate currents, and transformers (Art. 



446 ELECTRICITY AND MAGNETISM part ii 



480) to transform to low pressure at the consumers' 
houses. 

Example. — The City of London Electric Lighting Company 
generates alternate currents at a little over 2000 volts at 
its power-house on the south side of the Thames, and 
sends these currents through the feeders to suh-stations 
in the city, where they are transformed down to currents 
twenty times as large at a pressure of 100 volts ; at which 
low pressure they supply the network of mains and house 
branches, which are laid in conduits under the streets. 

Since the power of a current depends on the voltage 
at which it is supplied, the unit of supply recognized in 
law is based on the unit of power, the wait (Art. 435), 
and is defined as 1000 watts supplied for one hour (i.e. 
1 kilowatt-hour) or its equivalent. The maximum price 
which the English Board of Trade permits the supply 
company to charge the consumer for 1 unit is eightpence. 

441. Conditions of Electric Supply. — Electric energy 
is almost always supplied under one of two standard con- 
ditions, either — 

(a) at Constant Voltage, or 
(5) with Constant Current, 

In the former case the circuit is branched, and the 
current is supplied (usually at 100 volts) to all the lamps 
or motors in parallel (Art. 409), each lamp, etc., being 
independent of all others; and the current varying pre- 
cisely in proportion to the demand. 

In the latter case, seldom used except for strings of 
arc-lamps, the circuit is undivided, and the current 
(usually 10 amperes) flows through all the lamps in series 
(Art. 168). If lamps are turned out (by short-circuiting 
them) the voltage must be reduced to keep the current 
constant. 

442. Supply Meters. — Meters for measuring the 
supply to the houses of consumers are of several kinds. 

(rt) Chemical Meters. — The current or a known fraction 



CHAP, nil ELECTRIC SUPPLY METERS 447 

of it is passed through an electrolytic cell, there to 
deposit copper (Edison's method) or dissolve zinc 
(Jehl's improved Edison) . The amount of chemi- 
cal action is proportional to the ampere-hours. 

(b) Integrating Meters. — A uniformly -going clock 

drives a counting apparatus through an inter- 
mediate gear operated by the current (or by the 
watts), such intermediate gear being such that 
when current is small counting is small, when 
current large counting is large. An integrating 
disk-and-roUer, or an integrating cam, is a usual 
mechanism, its operation being controlled by the 
motion of an ampere-meter or wattmeter. 

(c) Motor Meters. — If the current passes through the 

armature of a small motor (Art. 443) having a 
constant field, having its speed controlled purely 
by fluid friction (by a fan) or by eddy-current 
friction (in a copper conductor revolving between 
magnet poles, Art. 457), its speed will at every 
instant be proportional to the current. Hence 
such a motor attached to a suitable counting-train 
of wheels will serve as a meter, the total number 
of revolutions being proportional to the ampere- 
hours. In Perry's meter (1898) the revolving part 
is a copper bell immersed in mercury, revolving 
around a central magnet pole (as the wire does in 
Fig. 201), and surrounded by an external S pole 
with ribbed projections to promote eddy-currents. 
In Schallenberger's meter for alternate currents 
the motor drives a fan. In Elihu Thomson's 
meter, which records the watt-hours, the revolving 
armature is of fine wire and high resistance, con- 
nected as shunt, while the fixed coils that serve as 
field-magnet take the whole current supplied. So 
the torque is proportional to the watts ; while a 
copper disk revolving between magnet poles, by 
its drag keeps the speed proportional to the torque. 



448 ELECTRICITY AND MAGNETISM part ii 

(d) Retarded Clocks. — Current may be made to act 
j upon the rate of a clock, by flowing in a coil 

under the pendulum bob if the latter is a magnet. 
I I Any force added thus to gravity or subtracted 

I from it will cause the clock to gain or lose. Ayr- 

i ton and Perry proposed to measure the supply 

by the total time gained or lost by a clock. In 
I Aron's meter, of which this is the principle, there 

i ; is a double clock with tw^o pendulums, only one 

I ! of which is acted on by the current. A train of 

i ' counting wheels is geared to record the diiference 

between the two. 



Lesson XXXVIII. — Electric Motors (Electromagnetic 
Engines) 

443. Electric Motors. — Electromagnetic engines, or 
motors, are machines in which the motive power is de- 
rived from electric currents by means of their electro- 
magnetic action. In 1821 Faraday showed a simple case 
(Art. 393) of rotation produced between a magnet and a 
current of electricity. Barlow produced rotation in a 
star-wheel, and Sturgeon in a copper disk, when traversed 
radially by a current while placed between the poles of 
a horse-shoe magnet. In 1831 Henry, and in 1833 
Ritchie, constructed small engines producing rotation by 
electromagnetic means. Fig. 230 shows a modification 
of Ritchie's motor. An electromagnet DC is poised upon 
a vertical axis between the poles of a fixed magnet (or 
electromagnet) SX. A current, generated by a suitable 
battery, is carried by wires which terminate in two 
mercury-cups, A, B, into which dip the ends of the coil 
of the movable electromagnet CD. When a current 
traverses the coil of CD it turns so as to set itself in the 
line between the poles XS, but as it swings round, the 
wires that dip into the mercury-cups pass from one cup 



CHAP. Tin 



ELECTRIC MOTORS 



449 



to the opposite, so that, at the moment when C approaches 
S, the current in CD is reversed, and C is repelled from 
S and attracted round to N^, the current through CD 
being thus reversed every half turn. In larger motors 
the mercury-cup arrangement is replaced by a commutator 
(devised by Sturgeon), consisting of a copper tube, slit 
into two or more parts, and 
touched at opposite points by 
a pair of metallic springs or 
" brushes." 

In another early form of 
motor, devised by Froment, 
bars of iron fixed upon the 
circumference of a rotating 
cylinder are attracted up to- 
wards an electromagnet, in 
which the cm-rent is automati- 
cally broken at the instant 
when each bar has come close 
up to its poles. In a third 
kind, an electromagnet is made 
to attract a piece of soft iron 
alternately up and down, with 
a motion like the piston of a 
steam-engine, which is con- 
verted by a crank into a rotatory motion. In these cases 
the difficulty occurs that, as the attraction of an electro- 
magnet falls off rapidly at a distance from its poles, the 
attracting force can only produce effective motion through 
very small range. Page from 1838 to 1850 designed 
various motors, in some of which iron plungers were 
sucked into hollow tubular coils of wire in which currents 
were caused to circulate at recurring intervals. 

In 1839 Jacobi propelled a boat along the river N'eva 
at the rate of 2| miles per hour with an electromagnetic 
engine of about one horse-power, worked by a battery of 
64 large Grove's cells. 
2 G 




Fig. 230. 



I 



450 ELECTKICITY AXD MAGNETISM part ii 

Jacobi appears to have been tlie first to recognize, 
about 1850, that the action of the electric motor is the 
simple converse of that of the dynamo or generator. 
Every magneto-electric generator or dynamo, such as is 
used in electric lighting, can also "work as a motor, giving 
out mechanical power when supplied with electric currents 
from some other source. Indeed the dynamos desigTied 
as generators make far more efficient motors than any 
of the older sorts of electromagnetic engines, which were 
little more than toys. 

In 1882 an u'on screw-boat capable of carrying 12 
persons, and driven by two such motors, with a power 
of about 3 horse-power, the current being furnished 
by 45 accumulators, was worked upon the Thames at a 
speed of 8 miles per hour. There is now a whole flotilla 
of electric launches on the Thames. 

444. Modern Electric Motors. — These are of two 
kinds: (1) those for use with continuous currents; (2) 
those for use with alternate currents. The former are 
constructed precisely on the plan of continuous current 
dynamos (Art. 462) having fixed field magnets and rotat- 
ing armature. The armatm'e is dragged round by the 
mutual action of the currents flowing in the copper 
conductors and the magnetic field in which the conductors 
lie. As explained in Art. 340, the force acting laterally 
on the conductors is proportional to the product of 
current and field. Hence if very powerful field-magnets 
are employed, a great torque (or turning moment) can be 
produced without requiring too great a current to be sent 
into the armature. The two factors of mechanical rotatory 
power are torque ( = angular force) and angular speed. If 
the field of the motor is maintained constant the torque 
is proportional to the current and the speed is proportional 
to the volts. If E is the electromotive-force generated 
(in direction opposing the current, see Art. 436) in the 
revolving armature, and C the current supplied to it, the 
electrical and mechanical expressions for the power 



CHAP. VIII EFEICIENCY OF MOTOES 451 

(watts) imparted to the armatiu-e are 

CE = anT, 

where n is revolutions per second, T the torque, and a a 
coefl&cient depending on the units chosen. 

If the armature current is supplied from mains at 
constant voltage, strengthening the magnetic field has 
the effect of slowmg speed, for equal power; and weak- 
ening the field quickens the speed. Alternate-current 
motors are described in Arts. 484 to 486. 

445. Efficiency of Motors. — If an ampere-meter be 
included in the circuit with a battery and a motor, it 
is found that the current is weaker when the motor is 
working than when the motor is standing still, and that 
the faster the motor runs the weaker does the current 
become. This is due to the E.M.F. generated in the 
revolving armature of the motor, which necessarily (Art. 
436) opposes the current. If the motor only exerts a 
small back electromotive-force it cannot utilize much of 
the power of the current. If V be the volts at which the 
current is supplied, and E the counter-electromotive-force 
generated by the motor, and C the current, then VC = 
gross power supplied, EC = nett power utilized ; and 
dividing the latter by former we get, as the electrical 

E 

efficiency of the motor, the ratio — . 

Example. — Suppose V = 100 volts and E = 90 volts, the 
efficiency will be 90 per cent. 

To make the efficiency as high as possible the motor 
should be so arranged (either by strengthening its mag- 
netic field, or by letting it run faster) that E is very 
nearly equal to V. In that case the motor will utilize 
nearly all the energy that flows to it. But since, by 
Ohm's law, the current is = (V — E)/r, where r is the 
internal resistance of the motor, it follows that when E 
becomes nearly equal to V the current will be reduced to 



452 



ELECTRICITY AND MAGNETISM part ii 




Fig. 231. 



a small fraction what it would be if the motor were at 
rest. The diagram (Fig. 231) makes the matter plainer. 
Let the line OV represent by its length the volts of 
supply V, and let OE represent the volts generated in 
the armature, proportional to speed and to field. On 
OV describe the square OYWX, and 
V K W draw the diagonal and the lines EH, 

KL. Then the area EVWH is pro- 
H portional to the gross power, being 
V(V — E), and area GLXH is propor- 
tional to the nett power, being 
E(Y— E). These two areas become 
more nearly equal, though both be- 
come small, when E is increased to 
be nearly equal to V. The area 
GLXH, the nett output of the motor, is a maximum 
when E = ^V ; but then the efficiency would be only 50 
per cent. 

The fact that when E is small the current is enormous 
is of great advantage in the starting of motors ; for at 
starting the great rush of current (which would destroy 
them if it lasted) produces a gTeat torque, and the naotor 
soon gets up speed and so cuts down the current to the 
working amount. 

446. Electric Locomotion. — Motors placed on cars 
or on separate locomotives can propel them singly or in 
trains provided the requisite power is supplied. This 
may be done in several ways : — 

(a) A battery of charged accumulators is carried on 

the car. 
(6) Current is furnished from a power-house, at some 
convenient point, to the rails on which the cars 
run, and which act as outgoing and return 
conductors, and are insulated. The cars (which 
have insulated wheels) pick up their currents 
from the rails. 
(c) Current is furnished from a power-house, to a third 



CHAP. VIII TRANSMISSION OF POWER 453 

rail insulated from earth. From this the current 
is picked up by the car, the ordinary rails being 
used as return conductor, 
(c?) Current is furnished from a power-house to an 
overhead line, with which the car makes contact 
as it runs by means of a trolley-wheel fixed on a 
long rod above the car. 
Method (a) is not economical, owing to weight of 
accumulators. Plan (6) is the one used by Siemens in the 
first electric tramway put down, in Berlin, in 1879. Plan 
(c) is used in several heavy electric railroads in England, 
to furnish current to locomotives of 200 to 400 horse- 
power. Plan (c?) is used for tramways chiefly in the 
United States, where there are now (1894) thousands of 
miles of light roads so equipped. 

447. Electric Transmission of Power. — Power may 
be transmitted to great distances electrically from a 
generator at one end of the circuit to a motor at the other. 
A mountain stream may be made to turn a turbine which 
drives a dynamo or alternator, the currents from which 
are conveyed to some centre of population by insulated 
wires to the motor which reconverts the electrical power 
into mechanical power. Scores of such examples are now 
at work. In the striking demonstration at Frankfort, in 
1891, 140 horse-power was conveyed from the falls of the 
Xeckar at Lauffen, 117 miles away, through three wires 
only 4 millimetres in diameter, with a nett efficiency of 
74 per cent, including all losses. 

Fig. 232 illustrates the case of a simple transmission 
between two machines. In one the electromotive-force 
drives the current, in the other the electromotive-force 
opposes the current. The first acts as generator (by the 
principle of Art. 436), the second as motor. If their 
respective electromotive-forces are E^ and Eg the electrical 
efficiency of the transmission is the ratio E2/Ej. 

The power lost in the line by reason of its resistance 
is the chief difficulty to face in such transmissions, owing 



454 



ELECTRICITY AXD MAGXETISM part ii 



to the prohibitive price of copper for carrying large 
currents without overheating. The watts wasted m a line 
of resistance R are (Art. 439) = C'^R. The gross watts 
utilized are (Art. 435) = CVm, where Ym is the volts at 
the motor end. Hence the power that must be poured in 
to the sending end of the line C^R + CYm watts. Xow 
it will be obvious that one may keep the C^R loss constant 
and yet increase the power that is transmitted by increas- 




GENERATOR 



MOTOR 



Fior. 232. 



ing ^"m the voltage at the motor — using in fact a high- 
voltage motor, and of course a high-voltage generator to 
correspond. To put the matter in another way. Let 
Yg be the volts at the generator end of the line, 
(Yg — Ym)R will be = C. Xow we may keep C con- 
stant (and therefore the C^R loss constant) and yet in- 
crease the voltages, provided Yq — Y^ remains as 
before. 

Example. — Suppose a line of copper-wire 20 miles long has 
resistance of 100 ohms. A current of 6 amperes in it will 
waste 3600 watts or nearly 5 horse-power. To send 6 
amperes through 100 ohms requires a difference of 
potentials of 600 volts. Suppose Yg = 1000 and 
Vm = 400, Yg — y^i = GOO. The watts sent in are 
CVg = 6000, and the watts delivered are CYm = 2100. 
Of 8 horse-power put in only about 3^ are delivered, the 



CHAP. Tin THE ELECTEIC ARC 455 



efficiency being Vm/Vg = 40 per cent. Now suppose 
Vg increased to 2000 volts, and Vm to 1400. Vg — Vm = 
600, as before. C = 6 amperes, as before. C^R loss is 
3600 watts, as before. But watts sent in are now 12,000 
(over 16 H.P.), and tbe watts delivered are 8400 
(II5 H.P.). Whilst the efficiency is now 70 per cent. 

It is therefore clear that high voltage is the secret of 
success in the electrical transmission of energy, whether 
for lighting or povrer, to long distances. In the trans- 
mission of energy from the Falls of Tivoli to light the 
city of Rome sixteen miles away, a pressure of 5000 volts 
is successfully used. In the scheme for utilizing the 
power of Niagara Falls, now on the way, a voltage of 
30,000 is proposed. 



Lesson XXXIX. — Electric Light 

448. The Electric Arc. — If two pointed pieces of 
carbon are joined by wires to the terminals of a powerful 
voltaic battery or other generator of electric currents, 
and are brought into contact for a moment and then 
drawn apart to a short distance, a kind of electric flame 
called the arc or " voltaic " arc is produced between the 
points of carbon, and a brilliant light is emitted by the 
white hot points of the carbon electrodes. This phenome- 
non was first noticed by Humphry DaAy in 1800, and its 
explanation appears to be the following : — Before con- 
tact the difference of potential between the points is 
insufficient to permit a spark to leap across even jq^o ^ of 
an inch of air-space, but when the carbons are made to 
touch, a current is established. On separating the carbons 
the spark at parting volatilizes a small quantity of carbon 
between the points. Carbon vapour being a partial con- 
ductor allows the current to continue to flow across the 
gap, provided it be not too wide ; but as the carbon 
vapour has a very high resistance it becomes intensely 
heated by the passage of the current, and the carbon points 



456 



ELECTRICITY AND MAGNETISM part ii 



also grow hot. Since, however, solid matter is a better 
radiator than gaseous matter, the carbon points emit far 
more light than the arc itself, though they are not so hot. 
The temperature of the arc is simply determined by the 
temperature at which carbon volatilizes ; about 3500° C. 
according to YioUe. In the arc tlie most infusible sub- 
stances, such as flint and diamond, melt ; and metals such 
as gold and platinum are even vaporized readily in its 

intense heat. When the 
arc is produced in the air 
the carbons slowly burn 
away by oxidization. It is 
observed, also, that particles 
of carbon are volatilized off 
and torn away from the + 
electrode, which becomes 
hollowed out to a cup-shape, 
or crater, and if the gap be- 
tween the carbons is smaU 
some of these particles are 
deposited on the — elec- 
trode, which assumes a 
pointed form, as shown in 
Fig. 233. The resistance of the arc may vary, according 
to circumstances, from 0-2 ohm upwards, according to the 
length and section of the flame. The arc also exerts an 
opposing electromotive-force of its own, amounting to 
about 35 volts when continuous currents are used, and 
the arc is silent. When it becomes unstable and hisses, 
the back electromotive-force is much lower. The seat of 
this back electromotive-force is at the surface of the crater 
where the work of volatilizing the carbon is being done. 

To produce an electric light satisfactorily a minimum 
electromotive-force of 40 to 50 volts is necessary if con- 
tinuous currents are used. With alternate currents 30 to 
35 volts suffice. The usual current for arc lamps of 1000 
to 2000 candle power is from 5 to 10 amperes. With 




CHAP, Till ARC LAMPS 457 

weaker currents or smaller electromotive-forces it is im- 
practicable to maintain a steady arc. For search-lights 
on board ship and for lighthouses, arc lights of greater 
power are produced by using thicker carbons and supply- 
ing them with cm'rents of 20 to 100 or more amperes. 
The common size of carbon rod in use is 10 or 11 
millimetres in diameter : the consumption is roughly 1 
inch per hour, the + carbon consuming much faster than 
the — carbon. The internal resistance of the ordinary 
Daniell's or Leclanche's cells (as used in telegraphy) is 
too great to render them serviceable for producing arc 
lights. A battery of 40 to 60 Grove's cells (Art. 182) 
is efficient, but will not last more than 2 or 3 hours. A 
dynamo-electric machine (such as described in Arts. 461 
to 469), worked by a steam-engiue, is the generator of 
currents in practical electric lighting. The quautity of 
light emitted by an arc lamp differs in different directions^ 
the greatest amount being emitted (when the -f carbon 
is at the top) at an angle of about 45° downwards. Most 
of it comes from the white hot crater, very little from the 
negative point. In the alternate-current arc the carbon 
points are alike and emit equal light. The current must 
not alternate more slowly than 40 periods per second. 
The total quantity of light emitted, when the current is 
supplied at a fixed voltage, is not quite proportional to 
the current, but increases in a somewhat higher ratio. 
Doubling the current makes rather more than twice as 
much light. 

449. Arc Lamps. — Davy employed wood charcoal 
for electrodes to obtain the arc light. Pencils of hard 
gas-carbon were later introduced by Foucault. In all the 
more recent arc lamps, pencils of a more dense and homo- 
geneous artificial coke-carbon are used. These consume 
away more regularly, and less rapidly, but still some 
automatic contrivance is necessary to push the points of 
the carbons forward as fast as needed. The mechanism 
of the arc lamp should " strike " the arc by causing the 



458 



ELECTRICITY AND MAGNETISM part ii 



pencils to touch, and then separate them to the requisite 
distance, about 5 millimetres ; the mechanism should also 
^' feed " the carbons into the arc as fast as they are con- 
sumed, and it should also cause 
the points to approach or re- 
cede automatically in case the 
arc becomes too long or too 
short ; it should further bring 
the carbons together for an 
instant to strike the arc again 
if by any chance the flame goes 
out. Arc Lamps or "regula- 
tors," fulfilling these condi- 
tions, have been invented by a 
number of persons. The earli- 
est was invented in 1847 by 
W. E. Staite. Arc lamps may 
be classified as follows : -^ 

(a) Clockwork Lamps. — 
Fig. 234 shows the regulator 
of Foucault as constructed by 
Duboscq; in this lamp the 
carbon-holders are propelled 
by a train of clockwork wheels 
actuated by a spring. An 
electromagnet at the base, 
through which the current 
runs, attracts an armature and 
governs the clockwork. If the 
current is too strong the arma- 
ture is draw^n down, and the 
clockwork draws the carbons 
farther apart. If the current 
is weakened by the increase of the resistance of the arc as 
the carbons burn away, the armature is drawn upwards 
by a spring, and a second train of wheels comes into play 
and moves the carbons nearer together. Clockwork arc 




Fig 234 



CHAP. Till 



ARC LAMP MECHANISM 



459 



lamps have also been devised in which the weight of the 
carbon-holders drive the clockwork mechanism. Of this 
class was Serrin's lamp, which from 1855 to the present 
time has been largely used for lighthouses, and for the 
optical lantern. 

(b) Brake-wheel Lamps. — Another mechanism for reg- 
ulating the rate of feeding the carbon into the arc consists 
in the addition of a brake-wheel ; 
the brake which stops the wheel 
being actuated by an electro- 
magnet which allows the wheel 
to run forward a little when the 
resistance of the arc increases 
beyond its normal amount. In 
Fig. 235 B is the brake-wheel, 
L the lever which governs it, C 
an iron core of the coil S inserted 
in the circuit. When current is 
switched on, the core is drawn 
up, causing L to grip B and turn 
it a little, so parting the carbons 
and striking the arc. 

(c) Solenoid Lamps. — In this 
class of arc lamp one of the car- 
bons is attached to an iron 
plunger capable of sliding verti- 
cally up or down inside a hollow 
coil or solenoid, which, being 
traversed by the current, regu- 
lates the position of the carbons 
arc. 




Fig. 235. 



and the length of the 
Siemens employed two solenoids acting against one 
another differentially, one being a main-circuit coil, the 
other being a fine-wire coil connected as a shunt to the 
arc. The shunt coil acts as a voltmeter to watch the arc 
and feed the carbons forward when the volts rise above 
the normal, it being set to control the feeding mechanism. 
(d) Clutch Lamps. — A somewhat simpler device is 



460 



ELECTRICITY AND MAGNETISM paki 



that of employing a clutch to pick up the upper carbon- 
holder, the lower carbon remaining fixed. In this kind 
of lamp the clutch is worked by an electromagnet, through 
which the main current passes. If the lamp goes out the 
magnet releases the clutch, and the upper carbon falls by 
its own weight and touches the lower carbon. Instantly 
the current starts round the electromagnet, which causes 
the clutch to grip the carbon-holder, and raise it to the 
requisite distance. Should the arc grow too long, the 
lessening attraction on the clutch automatically permits 
the carbon-holder to advance a little. 

(e) Motor Lamps. — Sometimes little electric motors 
are used to operate the carbons automatically. 

450. Grouping of Arc Lamps. — If the condition of 
supply is constant voltage the arc lamps must be set in 
parallel; if the arc lamps are to be run in series, the 
same current flowing in succession through each of the 
lamps, then the supply must be of a current of unvarying 
strength. In this case a shunt circuit is neces- 
sary in each lamp. 

451. Electric Candles. — To obviate the 
expense and complication of such regulators, 
electric candles have been suggested. Fig. 237 
depicts Jahlochkoff's candle, consisting of two 
parallel pencils of hard carbon separated by 
a thin layer of plaster of Paris and supported 
in an upright holder. The arc plays across the 
summit between the two carbon wicks. In 
order that both carbons may consume at equal 
rates, alternating currents must be employed. 

452. Incandescent Lamps or Glow-Lamps. 
— Arc lamps of an illuminating power of less 
than 100 candles are very unsteady and un- 
economical. For small lights it is both simpler 

and cheaper to employ a thin continuous wire or filament 
of some infusible conductor, heated to whiteness by 
passing a current through it. Thin wires of platinum 



Fig. 236. 



CHAP. Tin GLOW-LAMPS 461 

have repeatedly been suggested for this purpose, but 
they cannot be kept from risk of fusing. Iridium wires 
and thin strips of carbon have also been suggested 
by many inventors. Edison in 1878 devised a lamp 
consisting of a platinum spiral combined with a short- 
circuiting switch to divert the current from the lamp 
in case it became overheated. Swan in February 1879 
publicly showed a carbon wire lamp in a vacuous bulb. 
Edison in October 1879 devised a vacuum lamp with a 
coiled filament made of lamp black and tar carbonized. 
Swan in January 1880 prepared filaments from cotton 
thread parchmentized in sulphuric acid, and afterwards 
carbonized. Edison in 1880 substituted a flat strip of 
carbonized bamboo for a filament. Lane Fox in 1879 
used prepared and carbonized vegetable fibres. Crookes 
used a filament prepared from silk or vegetable matter 
parchmentized with cuprammonic chloride. 

Modern glow-lamps mostly have thin carbon wires 
prepared from parchmentized cellulose, which is then 
carbonized in a closed vessel. Sometimes the filaments 
are " flashed " over with surface carbon by being moment- 
arily heated electrically in a carbonaceous atmosphere. 
They are mounted upon platinum supports in a glass 
bulb through which the platinum wires pass out, and 
into which they are sealed, the bulbs being afterwards 
exhausted of air and other gases, the vacuum being made 
very perfect by the employment of special mercurial 
air-pumps. The bulbs should be heated during exhaus- 
tion to drive out residual gases. Carbon is the only 
suitable material for the conductor because of its superior 
infusibility and higher resistance. It also has the 
remarkable property, the reverse of that observed in 
metals, of offering a lower resistance when hot than 
when cold. Two common forms of glow-lamp are 
shown in Fig. 237 ; the typical form used by Swan in 
England, and the typical form perfected by Edison in 
America. The resistance of such lamps varies accord- 



462 



ELECTRICITY AND MAGNETISM part ii 



ing to size and length of the filament. A modern 16 
candle-power lamp for use on a 100-volt circuit will 
take about 0-6 ampere. That is to say, its resistance 
when hot will be about 166 ohms (or over 200 ohms when 
cold), and it will absorb about 
60 w^atts. This is at the rate 
of less than 4 watts per candle. 
Used so, it will last on the 
average over 1000 hours of 
burning. Lamps are made to 
give equal light and use less 
current, by using a thinner and 
rather shorter filament; but 
then they do not last so long. 
The surface disintegrates in 
time if forced to emit too much light. The power required 
to operate 12 such 60-watt lamps will be 720 watts, or 
nearly 1 horse-power. 

The following table gives some data about a 10-candle 
50-volt lamp if used at different voltages. 




Fig. 23T. 



Volts. 


Amperes. 


Watts. 


Candle- 
power. 


Watts per 
candle. 


Probable 
life (.hours). 


48 


0-77 


37 


8 


4-3 


3200 


50 


0-81 


40-5 


10 


4-05 


1500 


53 


0-87 


46-4 


145 


3-2 


800 


55 


0-92 


50-6 


18-5 


2-7 


480 


58 


0-99 


57-5 


25-5 


2-2 


250 


61 


1-06 


64-7 


35-5 


1-8 


150 



The light increases as about the sixth power of the 
volts ; the energy consumed is only as the second power. 
But raising the volts a little shortens the life enormously. 

For special lamps of larger candle-power, up to 800 or 
1000, thin filaments cannot be used. In these flat strips 
or thick wdres of carbon are used ; they give out, for equal 
expenditure of power, much less light than an arc lamp. 



CHAP. Tin THREE-WIRE SYSTEM 463 

453. Grouping of Glow-Lamps. — Glow-lamps are 
usually grouped in parallel (Fig. 238) between mains 
kept at constant voltage. A common value for the 
difference of potential 

between the + and — — i I ' I 1 F" ~ 

mains is 100 volts. The V) |i jA |i jA fi 
current in the mains I II I I 
subdivides and flows ' 

through each lamp in- 
dependently. When any lamp is switched on it does not 
diminish the current in the others, but by opening an 
additional path simply causes proportionately more current 
to flow from the source of supply. The method of 
grouping in series (Art. 168) is seldom used for glow- 
lamps ; each lamp then requires an automatic cut-out to 
prevent the rest of the row from being extinguished in 
case one lamp goes out. 

Three-wire systems, in which a third or neutral wire is 
introduced between the -f and the — main, have been 

devised to enable 

:^-.| 1 , — I 1 + higher voltages to be 

used, and thereby 
enable twice as many 
lamps to be lit with 
little additional ex- 
penditure in copper. 
To render the lamps 
on one side of the 
circuit (Fig. 239) independent of those on the other, 
in case an equal number do not happen to be switched 
on at the same time, the middle wire (which only need 
be thick enough to carry a current equal to the difference 
between the currents in the two outer wires) is carried 
back to the station and kept at mean potential between the 
two outer wires by the use of two dynamos instead of one. 




CHAPTER IX 

INDUCTANCE 

Lesson XL. — Mutual Induction 

454. Mutual Induction. — Mutual induction between 
two circuits, a primary and a secondary, was briefly 
considered in Art. 224. Let us now consider the electro- 
motive-forces so induced. Suppose the primary coil to 
have Sj^ spirals, and the secondary coil S2 spii'als. At 
first let them be so arranged (by use of an iron core or 
by geometric juxtaposition) so that all the magnetic lines 
evoked by the primary coil pass through all the spirals of 
the secondary coil ; both coils being placed close together 
upon a suitable core of laminated iron. 

By Art. 377 the magnetic flux due to current C in 
the primary coil will be 

N = 47rCS/ilOZ, 

where Z is the reluctance (Art. 376) of the magnetic 
circuit. The total amount of cutting magnetic lines by 
the Sg spirals of the secondary, when current C is turned 
off or on, will be 

S2N = 47rCSiS2/10Z. 

Hence it follows that the amount of cutting of mag- 
netic lines {i.e. the induction in the secondary circuit) 
due to turning on or off 10 amperes (=1 C.G.S. unit of 
current) in the primary, will be ^irS-^^f^- This quantity 
464 



CHAP. IX MUTUAL INDUCTION 465 

is denoted for brevity by the symbol M. If the primary 
and secondary coils are not so arranged that all the mag- 
netic lines due to the one pass through the spirals of the 
other, then M will have a less value than ^ttSj^So/M. 

The practical unit for coefficients of mutual induction 
is the same as for those of self-induction, namely the 
henry (Art. 351), and is 10^ C.G.S. units. Hence to 
bring M to henries we must divide the above value by 10^. 

If the current in the primary is varying at the rate 
dC/dt, the electromotive-force Eg thereby induced in the 
secondary circuit will be 

E= -M-dC/dt, 

where E will be in volts if M is expressed in henries, C 
in amperes, and t in seconds. 

The value of M for the small induction coils used 
in telephone work is usually about 0-01 henry; for a 
E-uhmkorff coil capable of giving a spark 10 centimetres 
long it may be as much as 5 henries. 

Example. — Suppose in a spark-coil the value of Mis 8 hen- 
ries, and the primary current changes by an amount of 
1 ampere in one ten-thousandth of a second (owing to 
the quick-acting break) , the electromotive-force induced 
in the secondary during that ten-thousandth of a second 
will be 80,000 volts. 

To measure a coefficient of mutual induction, there are 
several methods, some of which depend on the use of Wheat- 
stone's bridge ; but the best method is one due to Carey 
Foster. In this the quantity of electricity discharged 
from a condenser of known capacity K shunted by a re- 
sistance p in the primary circuit is balanced against the 
quantity discharged in the secondary circuit by regulating 
a resistance q in the latter. Then M = Kpq. 

455. Induced Currents of Higher Orders. — Joseph 
Henry, an independent discoverer of magneto-electric 
induction, discovered that the variations in the strength 
2 H 



466 ELECTRICITY AND MAGNETISM part ii 

of the secondary current could induce tertiary cui'rents 
in a third closed circuit, and that variations in the ter- 
tiary currents might induce currents of a fourth order, 
and so on. A single sudden primary cm-rent produces 
two secondary currents (one inverse and one direct), each 
of these produces two tertiary currents, or four tertiary 
currents in all. But with alternating or periodic there 
are the same number of secondary and tertiary fluctua- 
tions as of primary; but the currents of the second, 
fourth, etc. orders will be inverse in the direction of their 
flow to those of the first, third, fifth, etc. 

456. Lenz's Law. — In Art. 223 it was explained 
how an increase in the number of magnetic lines through 
a circuit (as by pushing in a magnet) tended to set up an 
inverse current, or one flowing in such a direction as is 
opposed to the magnetism. Similarly a decrease in the 
magnetic lines (as by withdrawing the magnet) tends to 
set up currents that will pull the magnet back. Again, 
in Art. 379, it was laid down that a circuit traversed by 
a current experiences a force tending to move it so as to 
include the greatest possible number of magnetic lines-of- 
force in the embrace of the circuit. But if the num- 
ber of lines be increased, during the increase there 
will be an opposing (or negative) electromotive-force set 
up, which will tend to stop the original current, and 
therefore tend to stop the motion. If there be no cur- 
rent to begin with, the motion will generate one, which 
being in a negative direction, will tend to diminish the 
number of lines passing through the circuit, and so stop 
the motion. Lenz, in 1834, summed up the matter by 
saying that in all cases of electromagnetic induction the in- 
duced currents have such a direction that their reaction tends 
to stop the motion ichich produces them. This is known as 
Lenz's law : it is a particular case of the more general 
law applicable to all electromagnetic systems, namely, 
that every action on such a system, which, in producing a 
change in its configuration or state, involves a transforma- 



CHAP. IX EDDY-CURRENTS 467 

tion of energy, sets up reactions tending to preserve unchanged 
the configuration or state of that system. (Compare Arts. 
204 aiid'379.) 

457. Eddy-Currents Induced in Masses of Metal. — 
In 1824 Gambey found that a compass-needle oscillating 
in its box came to rest sooner if the bottom of the 
box were made of metal than if of wood. Arago in- 
vestigated the matter, and found a copper plate under 
the needle most effective in damping its motions. He 
then rotated a copper disk in its own plane underneath a 
compass-needle, and found that the needle was dragged 
round as by some invisible friction. A copper disk sus- 
pended over a rotating magnet was found to be dragged 
by it. Attempts were made to account for these pheno- 
mena — known as Arago' s rotations — by supposing there 
to be a sort of magnetism of rotation, until Faraday 
proved them to be due to induction. A magnet moved 
near a solid mass or plate of metal induces in it ciu-rents, 
which, in flowing through it from one point to another, 
have their energy eventually frittered down into heat, 
and which, while they last, produce (in accordance with 
Lenz's law) electromagnetic forces tending to stop the 
motion. These currents, circulating wholly within the 
metal, are called eddy-currents. If a cube or ball of 
good conducting metal be set 
spinning between the poles of 
such an electromagnet as Fig. 
182, and the current be sud- 
denly turned on, the spinning 
metal stops suddenly. In a 
copper disk revolving between 
the poles of a magnet (Fig. 240) Fig. 240. 

there is a pair of eddies in the 

part passing between the poles, and these currents tend to 
pull the disk back. In fact, any conductor moved forcibly 
across the lines of a magnetic field experiences a mechani- 
cal resistance due to the induced currents which oppose 




468 ELECTKICITY AND IVIAGNETISM part ii 

its motion. Foucault showed* that if, by sheer force, a 
disk be kept spinning between the poles of a powerful 
electromagnet it will become hot in consequence of the 
eddy-currents induced in it. 

The eddy-current drag on a moving conductor (some- 
times called the magnetic friction) is a force proportional 
to the speed and proportional to the square of the mag- 
netic field ; for the force (Art. 340) is proportional to the 
product of field and current, and the current (circulating 
round a given path) is proportional both to field and to 
speed. Hence eddy-current drag is employed in some 
forms of electric supply meter (Art. 442) to control the 
speed of the moving part. 

Alternating electric cm-rents also set up eddy-currents 
in masses of metal near them ; for this reason the ii'on 
cores of transformers (Art. 480) and of dynamo arma- 
tures (Art. 463) must be carefully laminated, otherwise 
there will be heating and waste of energy. 

Further, eddy-currents in any mass of metal between 
a primary and a secondary circuit vnll tend to set up 
in the secondary tertiary electromotive-forces opposing 
those set up by the primary. Hence interposed sheets of 
m.etal act as induction-screens. 



Lessox XLL — Self-induction 

458. Self-induction. — It has been pointed out in 
Art. 224 how when a ciu-rent in a ch'cuit is increasing or 
diminishing, it exercises an inductive effect upon any 
neighboming circuit ; this inductive effect being due to 
the change in the magnetic field surrounding the varying 
current. But since the magnetic lines surrounding a 
current may, as they move inwards or outwards from the 
wire, cut across other parts of the same circuit, it is evident 

* Hence some writers call the eddj'-currents " Foucault's currents,"' 
thougli the}^ were known years before Foucault's experiments were made. 



CHAP. IX SELF-INDUCTION 469 

that a current may act inductively on itself. The self- 
inductive action is great if the circuit consists of a coil of 
many turns, and is still greater if the coil possesses an 
iron core. Suppose a coil of wire to possess S spirals, and 
that it generates a magnetic flux through these spirals of 
N lines when current C is turned on. Then it is clear 
that turning on the current will have the same effect as if 
a magnet of N lines were suddenly plunged into the coil ; 
and turning off the current will have the same effect as if 
the magnet were suddenl}' withdrawn. N"ow (Art. 22.5) 
the current induced by plunging a magnet into a coil is 
an inverse current tending to push it out, while that 
induced by withdrawing the magnet is a direct current, 
tending to attract it back. It follows that the self- 
induced electromotive-force on turning the current on will 
tend to oppose the current, and prevent it growing as 
quickly as it otherwise would do, while that induced on 
stopping the current will tend to help the current to 
continue flowing. In both cases the effects of self- 
induction is to oppose change : it acts as an electro- 
magnetic inertia. 

In the case supposed above, where the coil has S turns, 
the total cutting of magnetic lines in the operation will 
= S X N, provided all the lines thread through all the 
spirals. Let the symbol L be used to represent the total 
amount of cutting of lines by the circuit when a current 
of 1 ampere is suddenly turned on or off in it. Clearly 
L X C = S X N. This quantity L is called " the induct- 
ance " of the circuit. It was formerly called "the 
coefficient of self-induction " of the circuit. The unit of 
induction is called the henry, and corresponds to a 
cutting of 10^ magnetic lines when 1 ampere is turned on 
or off. 

Since (in circuits without iron cores) N is proportional 
to S, it follows that L is proportional to S^. Or since 
(see Art. 377) N = 47rCS/10Z, and the total cutting of 
lines by the S spirals (if all the lines pass through all the 



470 ELECTRICITY AND MAGNETISM part ii 

spirals) is S x N, hence the induction when 10 amperes 
are turned on or off will be 

L = 47rSVZ, 

which may be expressed in henries by dividing by 10^. 
If all the lines do not pass through all the spirals the 
value of L will be less than this. 

The self-induced electromotive-force will depend upon 
the rate at which the current is changing ; for if the total 
cutting SN take place in time t, it follows (Art. 225) 
that : — 

E= -SN/^= -LC/t. 

But since the rate at which the current changes is not 
uniform, E is also not uniform. If in an element of time 
dt the current charges by an amount dC, the rate of charge 
of the current is dC/dt, and the self-induced electromotive- 
force is = — L • dC/dt. 

The formal definition of the henry (Art. 354) is based 
on the above expression in order that it may apply to 
circuits with iron cores as well as to circuits without 
them. 

The energy of the magnetic field surrounding the 
current is equal to ^LC^, since while the field is growing 
up to have LC lines in total, the average value of the 
current is iC. 

To measure a coefficient of self-induction there are 
several methods : — 

(a) Alternate- Current Method. — The volts V required 
to send current C at frequency n through coil having 
resistance R and coefficient of self-induction L are 



V = C VR^ -t- ^Tr'^n^U' ; or, if the resistance is negligible, 

V = 27rnCL, whence L = Y/27rnC (see Art. 472). 

(h) Bridge Methods. — Of several bridge methods the 
best is Maxwell's. Let balance be obtained in usual 
way ; key in battery circuit being put down before key 
in galvanometer circuit (Art. 415). Then press the keys in 



CHAP. IX EFFECTS OF SELF-INDUCTION 471 

reverse order, when the presence of self-mduction in one 
of the four arms will upset balance, the needle giving a 
kick a proportional to the seK-induction. Now introduce 
in the same arm an additional small resistance r, such 
that when keys are again operated in the usual order 
there is a small permanent deflexion 8. If the periodic 
time of swing of the needle be T the following formula 
then holds : — L = Tr8/27ra. 

(c) SecoTimmeter Method. — Ayrton and Perry invented 
an instrument which alternately makes and breaks the 
battery circuit of the bridge and only aUows the galvan- 
ometer to be in operation during a short interval of time 
T immediately after each making of the battery circuit 
(the galvanometer at other times being short-circuited). 
As the current is increasing during this interval, the 
self-induction L of a coil placed in one of the arms of the 
bridge acts as though there were an additional resistance 
r in that arm. The formula is then, L = Tr. As L is 
then the product of seconds and ohms, Ayrton and Perry 
proposed for the unit (now called the henry) the name 
of secohm. 

459. Effects of Inductance. — The presence of in- 
ductance in a circuit affects the currents in several ways. 
The special choking-effect on alternate currents is dealt 
with in Art. 474. The effects on battery currents are 
also important. So long as the current is not changing 
in strength inductance has no effect whatever ; but while 
the current is starting or while it is dying away the 
presence of inductance greatly affects it. In all cases 
inductance tends to oppose any change in the strength of 
the cm-rent ; as may be foreseen from Lenz's law (Art. 
456). When a current is increasing in strength induct- 
ance causes it to increase more slowly. When a current 
is dying away inductance tends to prolong it. 

The existence of inductance in a circuit is attested by 
the so-called extra-current, which makes its appearance 
as a bright spark at the moment of breaking circuit. If 



472 ELECTRICITY AND MAGNETISM part ii 

the circuit be a simple one, and consist of a straight wire 
and a parallel return wire, there will be little or no 
inductance ; but if the circuit be coiled up, especially if 
it be coiled round an iron core, as in an electromagnet, 
then on breaking circuit there will be a brilliant spark, 
and a person holding the two ends of the wires between 
which the circuit is broken may receive a shock, owing to 
the high electromotive-force of this self-induced extra 
current. This spark represents the energy of the mag- 
netic field surrounding the wire suddenly returning back 
into the circuit. The extra-cm-rent on " making " circuit 
is an inverse current, and gives no spark, but it prevents 
the battery current from rising at once to its full value. 
The extra-current on breaking circuit is a direct current, 
and therefore keeps up the strength of the cm'rent just 
at the moment when it is about to cease. To avoid the 
perturbing effects of inductance, resistance-coils are 
always coiled back upon themselves (Art. 414). 

Even when a circuit consists of two parallel straight 
wkes there is a magnetic field set up between them, 
giving inductive reactions. The coefficient of self-induc- 
tion for two wires of length I and radius a at an axial 
distance h apart in air is 

L = /(| + 41og,^y0-9; 

where L is in henries ; a, h and I in centimetres, and ^ i 
the permeability of the wire. 

460. Helmholtz's Equation. Time-constant. — From 
that which precedes it is clear that whenever a current 
is turned on there is a variable period while the current 
is growing up to the value which it will reach when 
steady, namely the value as determined by Ohm's law. 
But during the variable period Ohm's law is no longer 
applicable. 

Von Helmholtz, who investigated mathematically the 
effect of self-induction upon the strength of a current. 



CHAP. IX GROWTH OF CURRENT 473 



deduced the following important equations to express the 
relation between the inductance of a circuit and the time 
required to establish the current at full strength : — 

Let dt represent a very short interval of time, and let 
the current increase during that short mterval from C to 
C + 6?C. The actual increase during the interval is c?C, 
and the rate of increase in streng-th is dC/dt. Hence, if 
the inductance be L, the electromotive-force of self-induc- 
tion will be — IjdQ/dt, and, if the whole resistance of the 
circuit be R, the streng-th of the opposing extra-current 

will be — -^ • — - during the short interval dt ; and hence 
Jtt dt 

the actual strength of current flowing in the circuit during 

that short interval instead of being (as by Ohm's law it 

would be if the cm-rent were steady) C = E/R, will be 

^^E_L dQ^ 
R ^' dt' 

To find out the value to which the current will have 
gTown after a time t made up of a number of such small 
intervals added together, requires an application of the 
integral calculus, which at once gives the following 

result : — 

(where e is the base of the natural logarithms). 

Put into words, this expression amounts to saying that 
after a lapse of t seconds the self-induction in a circuit on 
making contact has the effect of diminishing the strength of 
the current by a quantity, the logarithm of luhose reciprocal is 
inversely proportional to the inductance, and directly propor- 
tional to the resistance of the circuit and to the time that has 
elapsed since making circuit. 

The quantity L/R, the reciprocal of which appears 
in the exponential expression, is known as "the time-con- 
stant " or " persistence " of the circuit. It is the time 



474 



ELECTRICITY AND MAGNETISM paet ii 



required by the cm-rent to rise to a certain fraction, namely 
(e — l)/e, — or 0-634 — of its final value. 

A very brief consideration will show that in those 
cases where the circuit is so arranged that the inductance 
L is small as compared with the resistance R, so that the 

e J will vanish from 

the equation for all appreciable values of t. 

On the other hand if L is great compared with R, the 
current during its growth will be governed almost entkely 
by the inductance, and not by the resistance of the 
circuit, which will act as though its resistance were 
= L/^ 



time-constant is small, the term 



r 

1 / 


-SG^^^ 


V '• 


CURVE B 
Seconds 



These matters are graphically depicted in Fig. 241, in which 
there are two curves of rise of current. Consider a circuit having 
E = 10 volts, R = 1 ohm, L = 10 henries. The steady current will 

be 10 amperes ; but at the end 

Or- -; of 1 second, as may be calculated 

9-t ^ 'by Helmholtz's equation, the 

current is only 0*95 of an am- 
pere ! hi 2 seconds it is 1'81, 
in 5 seconds 3-95, in 10 seconds 
6' 34 amperes (see curve A) . At 
the end of a whole minute it is 
only 9' 975 amperes. Suppose 
now we increase the resistance 
to 2 ohms, and reduce the in- 
ductance to 5 henries. The 
final value of the current will 
be only 5 amperes instead of 10 ; 
but it will rise more quickly than before (see curve B). At the 
end of 1 second it will be 1'647 ampere, in 2 seconds 2"755, in 10 
seconds 4'91 amperes. We conclude that for all apparatus that 
is required to be rapid-acting (relays, telephones, chronographs, 
etc.) , it is much more important to keep down the inductance 
than the resistance of the circuit. We also see that the rule {k^t. 
407) so often given, about making the resistance of a battery 
equal to that of the rest of the circuit, is quite wrong for cases 
of rapid action. If the circuit has self-induction as well as 
resistance then it is better to group the cells of the battery so 
as to have higher resistance, namely put them all in series. 



2 4 



8 10 12 14 16 18 20 

Yis. 241. 



CHAP. IX EXTRA-CUERENT 475 

In fact everything goes on as though at time t after 
" make " there were two currents flowmg in opposite 
dii-ections at once ; one the ordinary current flowing from 
the first at full strength, the other the extra-current 

J] — R</L 

having the value - — e ; the actual current being the 

difference between the two. 

At " break " of circuit everything goes on as if, the 

ordinary current having dropped suddenly to zero, there 

was superposed an extra-current having the value 

E -'^/^ 
-f— € ; but here, since there is introduced into the 
K 

cii'cuit a resistance of unknown amount (the resistance 
along a spark being indefinite), the calculation becomes 
impracticable. We know that R is very great ; hence 
we know that the variation will be more sudden, and 
that the self-induced E.M.F. at " break" is much greater 
than that at " make." The self -induced E.M.F. would 
be represented by the expression Ef = Ee -^/'^. This 
expression should be compared with that for the E.M.F. 
of discharge of a condenser of capacity K through a 
resistance R (see also Art. 326), which is V^ = VoC-'/^^. 
From this it appears that in the case of a condenser dis- 
charge KR acts as the time-constant L/R does in the 
case of self-induction. 

The actual quantity of electricity conveyed by the 
" extra-current " is equal to that which would be con- 
veyed by current of strength E/R of lasting for time 
L/R; or = EL/R^. At the "make" of the circuit the 
retardation causes the flow of electricity to be lessened 
by the amount q = EL/R^. The energy which is stored 
up outside the wire while the current grows up from to 
its final value C is equal to ^qE = ^LC^^. 



CHAPTER X 

DYNAMOS AND TRANSFORMERS 

Lesson XLII. — Magneto-electric and Dynamo-electric 
Generators 




Fig. 242. 



461. Simple Magneto-electric Machines. — Fara- 
day's discovery of the induction of currents in wires 

by moving them across a 
magnetic field suggested the 
construction of magneto- 
electric machines to generate 
currents in place of voltaic 
batteries, and Faraday him- 
self constructed the first of 
such machines (Fig. 132) in 
1831. In the early attempts 
of Pixii (1833), Saxton, 
and Clarke, bobbins of insulated wu-e were fixed to an 
axis and spun rapidly in front of the poles of strong steel 
magnets. But, since the currents thus generated were 
alternately inverse and direct currents, a commutator 
(which rotated with the coils) was fixed to the axis to 
turn the successive currents all into the same direction. 
Fig. 242 illustrates the plan adopted by Sturgeon in 
1836, using a split tube of copper to commute the con- 
nexion to the outer circuit at each half turn. In the 
figure the wire coil is supposed to be spun around a longi- 
476 



CHAP. X MAGNETO-ELECTRIC MACHINES 



477 



/^ 


N 




( f 




i/a 


--\— 


{[{----') 


y% 




\<: ^ 


"^ 


^^§i^ 





Fig. 243. 



tudinal axis ; the upper portion coming towards the 
observer. The arrows show the direction of the induced 
cuiTents delivered by the 
commutator to the contact- 
springs or trushes. The little 
magneto - electric machines, 
still sold by opticians, are on 
this principle. Holmes and 
Yan Malderen constructed 
more powerful machines, the 
latter combining around one 
axis sixty-four separate coils rotating between the poles 
of forty powerful magnets. 

In 1856 Werner Siemens devised an improved arma- 
ture, in which the coils of wire were wound shuttle-wise 
upon a grooved iron core, which concentrated the mag- 
netic lines in a powerful field between the poles of a series 
of adjacent steel magnets. The 
next improvement, due to Wilde, 
was the employment of electro- 
magnets instead of steel magnets 
for producing the field in which 
the armature revolved ; these 
electro-magnets being excited by 
currents furnished by a small 
auxiliary magneto-electric ma- 
chine, also kept in rotation. If 
instead of commuting the cur- 
rents the ends of the revolving- 
coil are connected to a pair of contact rings, on each of 
which presses a brush, the machine will deliver alternate 
currents. Fig. 243 illustrates a primitive form of alter- 
nator. It will be seen that if the induced E.M.F. in the 
wires as they move past the N pole towards the observer 
is from left to right, the two contact rings will alternately 
become -}- and — at each half turn. 

462 . Dynamo-electric Machines . — The name dynamo- 




Fig. 244. 



478 ELECTRICITY AND MAGNETISM part ii 

electric machine, or, briefly, dynamo, is given to any 
machine for converting mechanical power into electrical 
power by the operation of producing relative motion 
between magnets and conductors. The part which acts 
as magnet is termed the Jield-magneU In continuous-cur- 
rent generators it usually stands still; in some alternators 
it is made to revolve. Its function is to provide a large 
number of magnetic lines. The part which acts as the 
active conductor, cutting the magnetic lines and having 
electromotive-force induced in it is termed the armature. 
In continuous-current generators, the armature revolves 
between the poles of the field-magnet. In some alterna- 
tors it is stationary. In the early machines the magnet- 
ism of the field magnets was independently excited. 
Various suggestions were made by Hjorth, Murray, S. A. 
Varley, and others to use the currents generated in the 
armature to excite the field-magnets. This was done in 
1867 by Varley, Werner Siemens, and Wheatstone ; the 
small current induced by the feeble residual magnetism 
being sent around the electromagnet to exalt its magnet- 
ism, and prepare it to induce still stronger currents. To 
machines so rendered self-exciting Werner Siemens gave 
the distinguishing name of dynamo-electric machines or 
generators, to distinguish them from the generators in 
which permanent steel magnets are employed. In either 
case the current is due to magneto-electric induction ; and 
in either case also the energy of the currents so induced 
is derived from the dynamical power of the steam-engine 
or other motor which performs the w^ork of moving the 
rotating coils of wire in the magnetic field. But the 
name has been extended to all generators, whether self- 
exciting or not. In all of them the electromotive-force 
generated is proportional to the number of turns of wire 
in the rotating armature, and to the speed of revolution. 
When currents of small electromotive-force, but of con- 
siderable strength are required, as for electroplating, the 
rotating armatures of a generator must be made with 



CHAP. X DYNAMOS 479 

small internal resistance, and therefore of a few turns of 
stout wire or ribbon of sheet copper. For producing 
currents at a high electromotive-force the armature must 
consist of many turns of wu'e or of rods of copper suitably- 
connected, and it must revolve in a very powerful mag- 
netic field. 

463. Continuous-current Dynamos. — The dynamos 
of different makers differ in the design of their field- 
magnets and in the means adopted for securing conti- 
nuity in the induced currents. Most continuous-current 
dynamos have a simple field-magnet with two poles : 
but many large machines are made with four, six, or eight 
poles. But the modern armature is complex. A simple 
coil, such as Fig. 242, with its 2-part commutator will not 
yield a steady current ; for twice in each revolution the 
E.M.F. dies away to zero. The coils must be grouped so 
that some of them are always active. In most dynamos 
the armature winding is constructed as a closed coil, 
the wu^e being wound on a ring core of iron (Pacinotti's 
core with teeth, Gramme's core without teeth), or as a 
drum over a cylindrical core (Siemens's or Von Hefner's 
plan), or having the coils arranged flat as a disk 
(Desrozier's plan). In all these cases the convolutions are 
joined up so that (like the ring winding in Fig. 190) the 
coil is endless. If the current is brought in at one side 
of such a coil and taken out at the other side there will 
be tAvo paths through the coil. As the coil spins between 
the poles of the magnet the electromotive-forces induced 
in the ascending and descending parts will tend to send 
the currents in parallel through these parts ; and con- 
sequently contact-brushes must be set to take off the 
currents from the revolving coils at the proper places. 
The brushes are, however, set in contact not with the 
coils themselves but with a commutator, Fig. 244, consist- 
ing of a number of copper bars, insulated from one 
another, and joined on to the armature coil at regular 
intervals. Consider, for example, a Gramme ring made 



480 



ELECTRICITY AND ^MAGNETISM part ii 



as it were of a number of bobbins wound upon a ring 
core of iron ^vire. Each bobbin constitutes one section of 
the winding, and they are all joined together, the end of 
one section to the beginning of the next, and each such 
junction is joined down to a bar of the commutator. 
The current cannot pass from one bar of the commutator 
to the next without traversing the intervening section of 




Fig. 245. 

the windings. The commutator revolves with the arma- 
ture ; while the brushes, which are clamped in suitable 
holders, press against its surface, and are set in such a 
position that the current passes into them with as little 
sparking as possible. It is found that to prevent spark- 
ing the brushes must be set a little in advance of the 
diameter that is symmetrical between the poles : for the 
current in each section of the winding is reversed as it 
passes under the brush, and for sparkless reversal needs to 



CHAP. X DYNAMO CALCULATIONS 481 

be moving at that instant in a magnetic field of sufficient 
streng-th. The cm-rent in the armatm-e exercises a mag- 
netizing action, and tends to distort the magnetic field in 
the direction of the rotation. To prevent serious distor- 
tion and sparking, the field-magnet is made very powerful 
and massive. The "brushes" that receive the current 
were originally bunches of springy wires : in modern 
machines they are built up of copper strip or copper 
gauze, or consist of small blocks of carbon. Fig. 245 de- 
picts a modern type of dynamo, having a vertical magnet 
of massive WTought iron magnetized by currents flowing 
in coils wound upon the two limbs. Below, between the 
polar surfaces which are bored out to receive it, is the 
revolving armature (in this case a drum-armature) with 
the commutator and brushes. The core of the armature 
is built up of thin iron disks lightly insulated from one 
another, to prevent eddy-currents. 

All continuous-current dynamos will run as motors 
(Art. 443), if supplied with current at the proper 
voltage. 

For fuller descriptions of dynamos, and technical details of 
construction, the reader is referred to the author's treatise on 

Dynamo-electric Machinery. 

464. Dynamo Calculations. — In a 2-pole dynamo 
if N be the total number of magnetic lines sent by the 
field-magnet through- the armature, S the number of wires 
or conductors in series on the armature, counted all 
round, and n the number of revolutions per second, the 
electromotive-force generated by the spinning armature 
wall be 

E = nSW/108, 

for the cutting per second of magnetic lines is proportional 
to each of these three quantities, and we divide by 10^ to 
bring to volts. As with batteries (Art. 171), so with 
dynamos, if there is an internal resistance r, the available 
2i 



482 ELECTRICITY AND MAGNETISM part ii 

volts at the terminals Y will be less than the whole volts 
generated by an amount equal to rC, the lost volts. 

V = E-rC. 

As the electrical efficiency of the machine is the ratio 
V/E, it is evident that r should be as low as possible. 

Example. — X dyuamo having N = 7,170,000, S = 120, running 
at 780 revs, per min. (= 13 revs, per sec.) will generate 
an electromotive-force of 111 volts. If r = 0'0.33 ohm, 
then when C = 210 amperes, ?'C = 7 volts. Hence V = 104 
volts. 

The current C which a dynamo yields depends on the 
resistance, etc., of the circuit it supplies. The maximum 
current it can supply is limited by several considerations, 
such as the heating of its parts, the sparking at the 
brushes, which becomes serious if too much current is 
drawn from the machine, the mechanical strength of its 
parts, and also the power of the driving-engine. 

The gross output of a dynamo is the number of 
amperes multiplied hj the total electromotive-force gene- 
rated, or CE. Tlie nett output is the number of amperes 
multiplied by the volts at terminals, or CV. These num-, 
bers are turned to horse-power by dividing by 746. 

The commercial efficiency of a dynamo is the ratio 
between the nett output and the mechanical power ap- 
plied to drive the machine. 

All the armature conductors of a dynamo are subject, 
when the machine is running, to a mechanical drag op- 
posing the rotation. This is due to the action between 
the magnetic field and the current (Art. 340). 

A little power is wasted by eddy-currents (Art. 457), 
and by hysteresis (Art. 368) in the armature core, and 
also a little by eddy-currents (Art. 463) in the moving 
masses of metal, so diminishing the efficiency : but in 
well-constructed machines such losses are slight. 

To calculate the field-magnet windings the formulae of 



WINDING OF FIELD-MAGNETS 



483 



Arts. 377 and 399 must be applied (see exercise 21 on 
Chap. v.). 

465. Excitation of Field-Magnets. — There are sev- 
eral modes of exciting the magnetism of the field-mag- 
nets, giving rise to the following classification : — 

1. Magneto Machine, with permanent steel magnets. 

2. Separately-excited Dynamo ; one in which the cur- 
rents used to excite the field-magnets are furnished by a 
separate machine called an " exciter." 

3. Separate-coil Dynamo, with a separate coil wound 
on the armature to generate the exciting current. 

4. Series-Dynamo, wherein the coils of the field-mag- 
net are in series with those of the armature and the 




s 


giiiii! [liiijji 








->^ 


^liiiiii 








1 snHsir 

"1 MAIN 





Fig. 24T. 



Fig. 248. 



external circuit (Fig. 246), and consist of a few turns of 
thick wire. 

5. Shunt-Dynamo, in which the coils of the field- 
magnet form a shunt to the main circuit ; and, being 
made of many turns of thin wire, draw off only a small 
fraction of the whole current (Fig. 247). 

6. Compound- Dynamo, partly excited by shunt coils, 
partly by series coils (Fig. 248). 

The last three modes are illustrated in the accompany- 
ing diagrams. Each variety of winding has certain 
advantages depending on conditions of use, 



484 



ELECTEICITY AND MAGNETISM part ii 



466. Characteristic Curves. — To study the behav- 
iour of various types of dynamo, Hopkinson devised 
the method of characteristic curces, wherein the two ele- 
ments of output — the volts and the amperes — are plotted 
out. If a series-dynamo is examined with amperemeter 
and voltmeter, while run at constant speed on various 
loads, its performance will be found to give a curve like 
OQY in Fig. 249, where the external volts are plotted 

vertically, the amperes hori- 




Fig. 249. 



zontaUy. This curve is the 
external characteristic. The 
volts rise as the current is 
increased, because of the 
increase of magnetization, 
but when this is near satura- 
tion they fall again because 
of internal resistance and 
sundry reactions. At any 
point such as Q the resist- 
ance of the external circuit 



is represented by the slope of the line QO {i.e. by the trig- 
onometrical tano-ent of the angle QOX), since tan QOX 
is equal to Q^I/OM ( = the volts divided by the amperes). 
If line OJ be di'awn so that tan JOX is equal to the 
internal resistance, then MX will represent the lost volts 
when the current = OM. Adding to QM a piece PQ = 
MX, we obtain PM as the corresponding value of the 
total electromotive-force. In this way, from the curve 
OY we can construct the total characteristic OE. It will 
be evident that if the total resistance {i.e. the slope of the 
line OP) be increased P will come down the curve toward 
O, and there Avill be a certain point at which any further 
increase in the slope will produce a sudden drop of volts 
and amperes to almost zero. This is a peculiarity of series- 
machines ; when running at a given speed they cease to 
yield any current if the resistance exceeds a certain criti- 
cal value, depending in each machine on its construction. 



CHARACTERISTIC CURVES 



485 




Fig. 250. 



For a shunt-dynamo the characteristic has a different 
form. When the machine is on open circuit, giving no 
current extern alh', the shunt circuit is fully at work 
exciting the magnet. The curve YV of volts at ter- 
minals begins at a high 
value, and as the current is 
increased by diminishing 
the resistance, the voltage 
gently falls. Part of this 
drop is due to internal resist- 
ance; part is due to arma- 
ture reactions and magnetic 
distortion ; and part to the 
reduction of the shunt 
current. If, as before, we 
draw O J to represent by its 
slope the internal resistance, we can find the lost volts MN" 
and add these on above Q, so obtaining P, a point on the 
total electromotive-force curve. This also drops slightly. 
If a shunt-dynamo be short-circuited, its magnetism is at 
once reduced to almost zero. To regulate the voltage of 
a shunt-dynamo a suitable rheostat (Fig. 206) may be 
introduced into its shunt circuit, to vary the exciting- 
current. 

467. Constant Voltage Machines. — For glow-lamp 
lighting, machines are needed that will maintain the 
voltage constant, whether the current going to the mains 
be small or large. The current that flows out of the 
machine will regulate itself exactly in proportion to the 
demand; more flowing when more lamps are turned on, 
provided the potential difference between the mains is 
kept constant. For this purpose neither a series-dynamo 
nor a shunt-dynamo (driven at a constant speed) will 
suffice ; though by hand-regulation, as above, a shunt- 
dynamo may be used. It will be noted that, while in 
shunt-machines the characteristic drops as the current 
is increased, in series-machines the curve rises. Conse- 



486 ELECTRICITY AND MAGNETISM part ii 

quently, by using a compound-winding, consisting of a 
shunt-winding (to give the proper voltage an open 
cii'cuit) and a few coils of thick wire, in series with the 
main circuit (to raise the excitation in proportion to the 
output), the voltage may be kept remarkably constant. 
By over-compounding with more series windings the dy- 
namo may be made to maintain a constant voltage at 
some distant point in the circuit. 

468. Constant Current Machines — Series Lighting. 
— To maintain an unvarying current in a series of 
lamps, as is frequently wanted for lighting with arc 
lamps (Art. 448), special dynamos are used known as 
arc-ligJiting machines. The best known of these are the 
Brush and the Thomson-Houston dynamos. Both have 
open-coil armatures (in which the coils are not grouped 
in a closed circuit), with special commutators, and auto- 
matic devices to regulate the output, the one by shunting 
the exciting current, the other by shifting the brushes. 
The current may thus be kept at 10 amperes, while the 
volts change (according to the number of lamps in circuit) 
from 50 to 2000 or more. 

469. Unipolar Machines. — There is another class 
of dynamo-electric machines, differing entirely from any 
of the preceding, in which a coil or other movable con- 
ductor slides round one pole of a magnet and cuts the 
magnetic lines in a continuous manner without any re- 
versals in the direction of the induced currents. Such 
machines, sometimes called " uni-polar " machines, have, 
however, very low electromotive-force, and are not prac- 
tical. Faraday's disk-machine (Fig. 132) belonged to 
this class. 



Lesson XLIII. — Alternate Currents 

470. Periodic Currents. — AVe have seen that the 
revolving of a simple coil in a magnetic field sets up 



CHAP. X ALTERNATING CURRENTS 487 

electromotive-forces, which change in direction at every 
half-tiu'n, giving rise to alternate currents. In each whole 
revolution there will be an electromotive-force which 
rises to a maximum and then dies away, followed imme- 
diately by a reversed electromotive-force, which also 
grows to a maximum and then dies away. Each such 
complete set of opei-ations is called a period, and the 
number of periods accomplished in a second is called the 
frequency or periodicity of the alternations, and is symbol- 
ized by the letter n. In 2-pole machines n is the same as 
the number of revolutions per second ; but in multipolar 
machines n is greater, in proportion to the number of pairs 
of poles. By revolving in a uniform field the electro- 
motive-forces set up are proportional to the sine of the 
angle through which the coil has turned from the posi- 
tion in which it lay across the field. If in this position 
the flux of magnetic lines through it were N, and the 
number of spirals in the coil that enclose the N lines be 
called S, then the value of the induced electromotive- 
force at any time t when the coil has turned through 
angle 6 {= 27rnt) will be 

E0 = 27r/iSNsin^--lO8, 

or, writing D for 27rnSN/10^, we have 

Ed = D sin e. 

In actual machines the magnetic fields are not uni- 
form, nor the coils simple loops, so the periodic rise and 
fall of the electromotive-forces will not necessarily follow 
a simple sine law. The form of the impressed waves 
will depend on the shape of the polar faces, and on the 
form and breadth of the coils. But in most cases we 
are sufficiently justified in assuming that the impressed 
electromotive-force follows a sine law, so that the value 
at any instant may be expressed in the above form, where 
D is the maximum value or amplitude attained by E, 
and 6 an angle of phase upon an imaginary circle of 



488 



ELECTRICITY AND MAGNETISM part ii 



reference. Consider a point P revolving clock-wise round 
a circle. If the radius of this circle be taken as unity, 
PM will be the sine of the angle 6, as measured from 0°. 
Let the circle be divided into any number of equal angles, 
and let the sines be drawn similarly for each. Then let 
these sines be plotted out at equal distances apart along 
the horizontal line, as in Fig. 251, giving us the sine 
curve. 

In Fig. 251 one revolution of P around the circle of 
reference corresponds to one complete alternation or cycle 




Fig. 251. 



of changes. The value of the electromotive-force (which 
varies between + D and — D as its maximum values) 
may be represented at any moment either by the sine 
PM or by projecting P on to the vertical diameter, giving 
OQ. As P revolves, the point Q will oscillate along the 
diameter. 

The currents which result from these periodic or 
alternating electromotive-forces are also periodic and 
alternating ; they increase to a maximum, then die away 
and reverse in direction, increase, die away, and then 
reverse back again. If the electromotive-force completes 
100 such cycles or reversals in a second, so also will the 
current. 

471. Virtual Volts and Virtual Amperes. — Meas- 
uring instruments for alternate currents, such as elec- 
tro-dynamometers (Art. 395), Cardew voltmeters (Art. 



CHAP. X LAG AND LEAD 489 

430), and electrostatic voltmeters (Art. 290) do not 
measure the arithmetical average values of the amperes 
or volts. The readings of these instruments, if first 
calibrated by the use of continuous currents, are the 
square roots of the means of the squares of the values. 
They measure what are called virtual amperes or virtual 
volts. The mean which they read (if we assume the 
currents and voltages to follow the sine law of variation) 
is equal to 0-707 of the maximum values, for the average 
of the squares of the sine (taken over either 1 quadrant 
or a whole circle) is i; hence the square-root-of-mean- 
square value is equal to 1^ v'2 times their maximum, 
value. If a voltmeter is placed on an alternating circuit 
in which the volts are oscillating between maxima of 
+ 100 and - 100 volts, it will read 70-7 volts ; and 70-7 
volts continuously applied would be required to produce 
an equal reading. If an alternate current amperemeter 
reads 100 amperes, that means that the current really 
rises to + 1414 amperes and then reverses to — 1414 
amperes ; but the effect is equal to that of 100 continuous 
amperes, and therefore such a current would be described 
as 100 virtual amperes. 

472. Lag and Lead. — Alternating currents do not 
always keep step with the alternating volts impressed 




Fig. 252. 

upon the circuit. If there is inductance in the circuit 
the currents wiU lag : if there is capacity in the circuit 
they will lead in phase. Fig. 252 illustrates the lag pro- 
duced by inductance. The impulses of current, repre- 



490 ELECTRICITY AND MAGNETISM part ii 

sented by the blacker line, occur a little later than those 
of the volts. But inductance has another effect of more 
importance than any retardation of phase ; it produces 
reactions on the electromotive-force, choking the current 
down. While the current is increasing in strength the 
reactive effect of inductance tends to prevent it rising. 
To produce a current of 40 amperes in a resistance of 1|^ 
ohms would require — for continuous currents — an 
E.M.F. of 60 volts. But an alternating voltage of 60 volts 
will not be enough if there is inductance in the circuit 
reacting against the voltage. The matter is complicated 
by the circumstance that the reactive impulses of electro- 
motive-force are also out of step : they are in fact exactly 
a quarter period behind the current. If an alternate cur- 
rent of C (virtual) amperes is flowing with a frequency 
of n cycles per second through a circuit of inductance L, 
the reactive electromotive-force* will be 27rnLC (virtual) 
volts. If, for example, L = 0-002 henry, n = 50 periods 
per second, and C = 40 amperes, the reactive electromo- 
tive-force will be 25-1 volts. Xow if we wish to drive 
the 40 (virtual) amperes not only through the resistance 
of 1\ ohms but against this reaction, we shall require more 
than 60 volts. But we shall not require 60 + 25-1 volts, 
since the reaction is out of step with the current. Ohm's 
law is no longer adequate. To find out what volts will 
be needed we have recourse to geometry. 

Plot out (Fig. 253) the wave-form OAhd, to correspond 
to the volts necessary to drive the current through the 
resistance, if there were no inductance. The ordinate 
a A may be taken to scale as 60. This we may call the 
current curve. Then plot out the curve marked — j^LC 
to represent the volts needed to balance the reaction of 

* This is calculated as follows. From Art. 458. E = 'LdC/dt. Now C 
is assumed to be a sine function of the time having instantaneous value 
Co sin 2-trnt ; where Cg is the maximum value of C. Differentiating this vnth. 
respect to time we get dC/dt = 2nnQQ cos lirnt. The " virtual " values of 
cosine and sine being equal we have for E the value 2n-wLC, but differing 
by J period fi-om the current in phase. 



PHASE DIFFERENCES 



491 



the inductance. Here p is written for 27rn. The ordi- 
nate at O is 25-1 ; and the curve is shifted back one 
quarter of the period : for when the current is increasing 
at its greatest rate, as at O, the self-inductive action is 
greatest. Then compound these two curves by adding 




Fig. 253. 

their ordinates, and we get the dotted curve, with its 
maximum at V. This is the curve of the volts that must 
be impressed on the circuit in order to produce the cur- 
rent. It will be seen that the current curve attains its 
maximum a little after the voltage curve. The current 
lags in phase behind the volts. If Od 
is the time of one complete period, the 
length va will represent the time that 
elapses between the maxima of volts 
and amperes. In Fig. 254 the same 
facts are represented in a revolving- 
diagram of the same sort as Fig. 251. 
The line OA represents the working 
volts R X C, whilst the line AD at right angles to OA 
represents the self-induced volts pLC. Com.pounding 
these as by the triangle of forces we have as the im- 
pressed volts the line OD. The projections of these 3 
lines on a vertical line while the diagram revolves 
around the centre O give the instantaneous values of 
the three quantities. The angle AOD, or <^, by which 
the current lags behind the impressed volts is termed the 




492 



ELECTRICITY AND MAGNETISM part ii 



angle of lag. However great the inductance or the fre- 
quency, angle ^ can never be greater than 90°. If 
OA is 60 and AD is 25-1, OD \vill be 65 volts. In 
symbols, the impressed volts M^ill have to be such that 
E^ = (RC)2 + {phC)'^. This gives us the equation : — 



C = 



VR2 + jw2L2 

The denominator which comes in here is commonly called 
the impedance. 

473. Maxwell's Law. — In Figs. 255 and 256 the 
angle of lag is seen to be such that tan ^ = jsLC/RC or 





/LC 



= j;L/R. And it is evident that the effect of the induct- 
ance is to make the circuit act as if its resistance instead 
of being R was increased to VR^ + p^U'. ^^ f^ct the alter- 
nate current is governed not by the resistance of the 
circuit but by its impedance. At the same time the cur- 
rent is lagging as if the angle of reference were not 6 but 
— cl>, so that the equation for the instantaneous values 
of C, when E = D sin 0, is 

^ ^ D sin (6 - <f>) 

\/R2 + p2L2 ' 

This is Maxwell's law for periodic currents as retarded 
by inductance. As instruments take no account of phase 
but give virtual values the simpler form preceding is 
usually sufficient. 

The effect of capacity introduced into an alternate 
current circuit is to produce a lead in phase, since the 
reaction of a condenser instead of tending to prolong the 



CHOKING COILS 



493 



current tends to drive it back. The reactance is therefore 

written as —1/pK, and the angle <^ will be such that 

tan <^ = - 1 //)K R. The impedance will be VW+lJp^. 

If both inductance and capacity are present, tan 





<^=(;;L — l/j9K)/R; the reactance will be joL — l/joK; 
and the impedance \/R-+ (j^L — l/pK)^. 

Since capacity and inductance produce opposite effects 
they can be used to neutralize one another. They exactly 
balance if lj = l/p^l\. In that case the circuit is non- 
inductive and the currents simply obey Ohm's law. 

474. Choking Coils. — It will be seen that if in a 
circuit there is little resistance, and much reactance, the 
current vvill depend on the reactance. For example if 
p( = '27rn) were, say, 1000 and L = 10 henries while R was 
only 1 ohm, the resistance part of the impedance would 
be negligible and the law would become 



c=- 

pL 

Self-induction coils with large inductance and small resist- 
ance are sometimes used to impede alternate currents, and 
are called choking coils, or impedance coils. 

If the current were led into a condenser of small 
capacity (say K = y1o microfarad, then l/j9K = 10,000), the 
current running in and out of the condenser would be 
governed only by the capacity and frequency, and not by 
the resistance, and would have the value — 



C = EpK. 
475. Alternate-current Power. 



If to measure the 



494 ELECTRICITY AND MAGNETISM part ii 

power supplied to a motor, or other part of an alternate 
current circuit, we measure separately with ampere- 
meter and voltmeter the amperes and volts, and then 
multiply together the readings we obtain as the apparent 
watts a value often greatly in excess of the true watts, 
owing to the difference in phase, of which the instruments 
take no account. The true power (watts) is in reality 
W = CVcos^, where C and V are the virtual values, and 
^ the angle of lag. But the latter is usually an unknown 
quantity. Hence recourse must be had to a suitable 
watt-meter ; the usual form being an electrodynamometer 
(Art. 438) specially constructed so that the high-resistance 
circuit in it shall be non-inductive. 

Whenever the phase-difference (whether lag or lead) 
is very large the current, being out of step with the volts, 
is almost wattless. This is the case with currents flowing 
through a choking coil or into a condenser, if the resist- 
ances are small. 

476. High Frequency Currents. — The reactive effects 
of inductance and capacity increase if the frequency 
is increased. The frequency used in electric lighting is 
from 50 to 120 cycles per second. If high frequencies 
of 1000 or more cycles per second are used the reactions 
are excessive. In such cases the currents do not flow 
equally through the cross-section of the conducting wire, 
but are confined mainly to its outer surface, even thick 
rods of copper offering great impedance. Even at a 
frequency of 100 the current at a depth of 12 millimetres 
from the surface is (in copper) only about } of its value 
in the surface layers. In iron wires the depth of the 
skin for | value is about 1 millimetre. For such rapid 
oscillations as the discharge of a Leyden jar, where the 
frequency is several millions, the conducting skin is prob- 
ably less than y^^ of a millimetre thick. Hollow tubes 
in such cases conduct just as well as solid rods of same 
outer diameter. The conductance is proportional not to 
section but to perimeter. 



CHAP. X ALTEENATE-CURKENT PHENOMENA 495 

Whenever a current is not distributed equally in the 
cross-section of any conductor there is a real increase in 
the resistance it offers ; the heating effect being a mini- 
mum when equally distributed. The fact that the 
oscillatory currents are greatest at the skin gives the 
strongest support to the modern view that the energy in 
an electric ch-cuit is transmitted by the surrounding 
medium and not through the wire (see Art. 519 on 
energy-paths). 

477. Alternate-current Electromagnets. — When an 
alternate current is sent through a coil it produces an 
alternating magnetic field. An iron core placed in 
the alternating field will be subjected to a periodic 
alternating magnetization. Electromagnets for alter- 
nate currents must have their iron cores laminated to 
avoid eddy currents ; and owing to their choking action 
are made with fewer turns of wire than if designed 
for continuous currents of equal voltage. They repel 
sheets of copper owing to the eddy currents which they 
set up in them ; the phase of these eddy currents being 
retarded by their self-induction. Elihu Thomson, who 
studied these repulsions, constructed some motors based 
on this principle. A solenoid, with a laminated iron 
plunger, if supplied with alternate currents at constant 
voltage, has the remarkable property of attracting the 
core with much greater force when the core is protruding 
out than when it is in the tube. This also is owing to 
the choking action. 



Lesson XLIV. — Alternate-current Generators 

478. Alternators. — The simple alternator (Fig. 243), 
with its two slip-rings for taking off the current, is merely 
typical. In practice machines are wanted which will 
deliver their currents at pressures of from 1000 to 5000 
volts, with frequencies of from 50 to 120 cycles per second. 



496 ELECTKICITY AND MAGNETISM part ii 

Slower frequencies are unsuitable for lighting, though 
applicable for power transmission. High voltages are 
common with alternate currents because (when using 
transformers) of the economy (Art. 447) thereby effected 
in the copper mains. Under these conditions almost all 
alternators are designed as multipolar machines ; and as 
the perfect insulation required in the armatures is more 
readily attained if these parts are stationary it is common 
to fix them, and instead to rotate the field-magnet. The 
latter is separately excited with a small continuous cur- 
rent led in through slip-rings. One advantage of alter- 
nate current machines over continuous cm-rent dynamos 
is that there is no commutator. 

Amongst the various types of alternators may be men- 
tioned the following: — (1) Magnet rotating internally 
and consisting of a number of poles, alternately 2^ and S, 
pointing radially outwards ; armature external, fixed, 
and consisting of a number of coils wound either upon 
an iron ring (Gramme), or upon inwardly projecting iron 
poles (Ganz), or set against the inner face of an iron core 
(Elwell-Parker), or embedded in holes just within the 
face of an iron core (Brown). In all cases where iron 
cores are used in armatures it is carefully laminated. 
(2) Magnet fixed externally and consisting of a number 
of alternate poles pointing radially inwards ; armature 
internal, revolving, consisting of a number of coils wound 
either upon the surface of a cylindrical iron core (West- 
inghouse, Thomson-Houston) or fixed upon radially pro- 
jecting poles (Hopldnson). (3) Magnet fixed externally 
and consisting of two crowns of alternate poles, alternately 
N and S, projecting toward one another and nearly meet- 
ing, so making a number of magnetic fields between them ; 
armature revolving, and without iron, consisting of a 
number of flat coils mounted together as a sort of star 
disk, revolve in the narrow gaps between the poles 
(Siemens, Ferranti). 

Another form, known as Mordey's alternator, largely 



ALTEKNATORS 



497 



used in England, is depicted in Fig. 259. The thin 
armature coils are fixed, in an external stationary ring, 
between two crowns of poles revolving on each side of 
them. These poles are, however, all X poles on one side, 
and all S poles on the other, being projections of two 
massive ii'on pole-pieces fixed on the shaft against a huge 




Fig. 259. 

internal bobbin, thus constituting a solid simple form of 
field-magnet. On the end of the shaft is a small continu- 
ous-current dynamo as exciter. 

In Fig. 260 is given a view of the central generating 
station for the electric lighting of the City of London. 
Two kinds of alternators (Thomson-Houston and jNIordey) 
are used. The cut shows one of the latter driven by an 
800 horse-power steam-engine. Each of these machines 
has 40 poles in each crown, and can deliver 250 amperes 
at 2200 volts. 
2k 



498 



ELECTRICITY AND MAGNETISM part ii 




CHAP. X COUPLING OF MACHINES 499 

479. Coupling of Alternators. — In the use of two 
or more alternators on one ciixuit a peculiarity arises that 
does not exist with continuous-ciu'rent dynamos, owing to 
diiierences of phase in the currents. If two alternators 
driven by separate engines are running at the same speed 
and at equal voltage, it will not do to join their circuits 
by merely switching them to the mains if they are not 
also in phase with one another ; or serious trouble may 
occur. In central station work it is usual to run several 
machines all in parallel. ]^ow if two machines are 
feeding into the same mains each 
is tenduig to send current back to 
tfie other; and if their electro- 
motive-forces are at any instant 
unequal, that with the greater will 
tend to send its current the oppo- 
site way through the other. To 
explain what occurs consider Fig. 
261, which is a revolving diagram 
of the same kind as Figs. 251 and 
254. If the two alternators are ^^' 

exactly in step, they will both be sending a pulse of current 
toward the mains at the same moment, but, so far as the 
circuit connecting them is concerned, these impulses will 
be exactly opposed. Let OA and OB represent these 
two exactly opposed impulses, j^ow suppose one of the 
two machines to gain a little on the other, OA shifting 
forward to OA'. The two electromotive-forces no longer 
balance, but will have a resultant OE tending to make a 
current oscillate through the two machines, this current 
being out of phase both with the leading machine A and 
with the lagging machine B. But this local current will 
itself lag a little in phase behind OE because of the in- 
ductance in its path. Let the phase of the current then 
be indicated by OC, which is set back a little. There is 
now a current surging to and fro between the two 
machines, and it is obviously more nearly in phase with 




503 ELECTRICITY AXD MAGXETISM part ii 

OA than with OB. This means that in the leading 
machine A the Tolts and amperes are move nearly in phase 
with one another than in the lagging machine B. Refer- 
ence to Arts. 436 and 445 will at once show that the cur- 
rent is helping to drive B as a motor, and that a greater 
mechanical effort will be thrown on A, which is acting 
more as a generator. Hence this interchange of cm-rent 
tends automatically to bring up the lagging machine and 
to load the leading machine. They will come back into 
phase. All alternators of good construction suitably 
driven will run together m parallel, even though their 
electromotive-forces are unequal. On the other hand, if 
two alternators are joined in series, the resulting current, 
when they are ever so little out of phase, tends to load the 
lagging machine and hasten the leading one till they get 
into complete opposition of phase, one running entirely as 
generator, the other entu'ely as motor. This is excellent 
for transmission of power from an alternator at one end 
of a line to a synchronous alternator at the other : the 
two machines keep step at all loads. But they will not 
run together in series if both are to act as generators, 
unless rigidly coupled together on the same shaft. 

To prevent accidents arising from too sudden a trans- 
fer of current between two machines it is usual in lighting 
stations to employ a syncl^ronizer, a device to indicate the 
phases of the alternations. When an alternator is to be 
switched into circuit (in parallel with one or more others) 
the operator does not turn the switch until (speed and 
volts being both right) the electromotive-force of the 
machine has come exactly into identical phase with that 
of the circuit into which it is to be introduced. 

Lesson XLY-. — Tran.-^formers 

480. Alternate-current Transformers. — Transform- 
ers are needed in the distribution of currents to a 
distance, because glow-lamps in the houses need low 



CHAP. X TEANSEOEMERS 601 

pressures of 50 to 100 volts, whilst for economy of copper 
in the mains it is necessary that the generators should 
work at high pressures of 1000 to 5000 or more volts. 
The principle of transformation was briefly touched in 
Art. 228. Alternate current transformers are simply 
induction-coils having well laminated iron cores, usually 
of thin, soft sheet-iron strips piled together, and shaped 
so as to constitute a closed magnetic circuit. Upon the 
cores are \Yound the primary coil to receive the alternat- 
ing current, and a secondary coil to give out other alter- 
nating currents. Usually the primary consists of many 
turns of fine copper wire, very well insulated, to receive 
a small current at high pressure ; and the secondary of a 
few turns of thick copper wire or ribbon, to give out a 
much larger current at low pressure. 

To transform down from about 2000 volts to 100 
volts, the ratio of the windings will be 20 : 1. Whatever 
the ratio of the voltages, the currents will be about in the 
inverse ratio, since, apart from the inevitable small losses 
in transformation, the power put in and taken out will be 
equal. Taking the above case of a transformer having 
20 : 1 as the ratio of its windings, if we desire to take out 
of the secondary 100 amperes at 50 volts, we must put 
into the primary at least 5 amperes at 1000 volts. 

In scattered districts a small transformer is provided 
for each house, the lamps being in the low-pressure cir- 



Alternator Lamps (^1 Lamps 

im)>y i am 

Low Pressure Mains 
Fig. 262. 

cuit. In cities large transformers are placed in sub- 
stations, from which issue the low-pressure mains dis- 
tributing the current to the houses. Fig. 262 shows 



502 ELECTRICITY AND MAGNETISM part ii 

in diagram the use of transformers on a distributing 
system. 

481. Elementary Theory of Transformers. — If the 
primary volts are maintained constant, the secondary 
volts "will be nearly constant also, and the apparatus 
becomes beautifully self-regulating, more current flow- 
ing into the primary of itself when more lamps are 
turned on in the secondary circuit. This arises from 
the choking effect of self-induction in the primary. If 
no lamps are on the secondary circuit the primary coil 
simply acts as a choking-coil. When all the lamps are 
on the primary acts as a working-coil to induce currents 
in the secondary. When only half the lamps are on 
the primary acts partly as a choking-coil and partly as a 
working-coil. 

Let Yj be the volts at the primary terminals, Yg 
those at the secondary terminals ; S^ the number of turns 
in the primary coil, Sg the number in the secondary; r^ 
the internal resistance in the primary, rg that of the 
secondary. Call the ratio of transformation k = 8^/82- 
The alternations of magnetism in the core will set up 
electromotive-forces E^ and Eg in the two coils strictly 
proportional to their respective numbers of turns (if there 
is no magnetic leakage) ; so Eg = Ej/A:; and since (apart 
from small hysteresis losses) E^Cj = EgCg, it follows that 
Cj = C2/A:. The volts lost in primary are r^^Cp those in 
secondary rgCg. Hence we may write 

Y, = E, + r,C,, 

Writing the first as Ej^ = Y^ — y-^C^ = Y^ — r^Cg/^, 
and inserting ^^/k for E^ in the second equation, we get 

which shows that ever}i:hing goes on in the secondary as 



CHAP. X TRANSrOEMATIONS OF CURRENTS 503 

though the primary had been removed, and we had sub- 
stituted for Yj a fraction of it in proportion to the wind- 
ings, and at the same time had added to the internal 
resistance an amount equal to the internal resistance of 
the primary, reduced in proportion to the square of the 
ratio of the windings. We also see that to keep the 
secondary volts constant the primary generator must be 
so regulated as to cause the primary volts to rise slightly 
when much current is being used. The currents in the 
two coils are in almost exact opposition of phase ; they 
reach their maxima at the same instant, flowing in oppo- 
site senses round the core. The efficiency of well con- 
structed transformers is very high, the internal losses 
being a very small percentage of the working load. 

482. Continuous-current Transformers (Motor-dyna- 
mos). — To transform continuous currents from one 
voltage to another it is necessary to employ a rotating 
apparatus, which is virtually a combination of a motor 
and a generator. For example, a motor receiving a cur- 
rent of 10 amperes at 1000 volts may be made to drive a 
dynamo giving out nearly 200 amperes at 50 volts. In- 
stead of using two separate machines, one single arma- 
ture may be wound with two windings and furnished 
with tw^o commutators ; the number of turns in the 
windings being proportioned to the voltages, and their 
sectional areas to the amperes. Such motor-dynamos are 
in use. The elementary theory of these is the same as 
that in Art. 481, E^ and Eg now standing for the electro- 
motive-forces respectively induced in the two windings 
on the revolving armature. 

483. Continuous-alternate Transformers. — Revolv- 
ing machinery equivalent to a combination of a con- 
tinuous-current dynamo and an alternator may be used 
to transform continuous currents into alternating, or 
vice versa, one part acting as motor to drive, the other 
as generator. In this case also two separate machines 
need not always be used. Fig. 263 represents in diagram 




Fiff. 263. 



504 ELECTRICITY AND MAGNETISM part ii 

a simple rotating armature having both a split-tube com- 
mutator to collect contin- 
uous currents, and a paii- 
of slip-rings or alternating 
currents. Such a machine 
may convert continuous 
currents into alternating, 
or alternating into contin- 
uous. Or it may act as 
a motor if supplied with 
either kind of cm-rent ; or 
may, if driven mechanically, generate both kinds of cur- 
rent at the same time. 



Lessox XL"\T^. — Alternate-current Motors 

484. Alternate-current Motors, — We have seen (Art. 
479) that one alternator can drive another as a motor, 
the two machines in series working in synchronism. 
There are two disadvantages in such motors — (i.) that 
they are not self-starting, but must be brought up to 
speed before the current is applied ; (ii.) that their field- 
magnets must be separately excited. Other forms of motor 
have consequently been sought. Ordinary continuous- 
current motors, if made with laminated iron magnets, 
will work, though not well, with alternating currents. 

The modern alternate-current motor has developed 
from the proposals of Borel (1887), Ferraris (1888), and 
Tesla (1888) to employ two or more alternating currents 
in different phases. 

485. Polyphase Currents. — It is obviously possible, 
by placing on the armature of an alternator two sep- 
arate sets of coils, one a little ahead of the other, to 
obtain two alternate currents of equal frequency and 
strength, but differing in phase by any desired degree. 
Gramme, indeed, constructed alternators with two and 



CHAP. X DI-PHASE AND TEI-PHASE WORKING 505 




with three separate circuits in 1878. If two equal alter- 
nate currents, differing in phase by one-quarter of a 
period, are properly combined, they can be made to pro- 
duce a rotatory magnetic field. And in such a rotatory 
field conductors can be set rotating, as was first 
suggested by Baily in 1879. Con- 
sider an ordinary Gramme ring 
(Fig. 264) wound with a continuous 
winding. If a single alternating 
current were introduced at the 
points AA' it would set up an 
oscillatory magnetic field, a N pole 
gi'owing at A, and a S pole at A', . . 

then dying away and reversing in 
direction. Similarly, if another '^' 

alternate current were introduced at BB', it would 
produce another oscillatory magnetic field in the BB' 
diameter. If both these currents are set to work but 
timed so that the BB' current is \ period behind the 
A A' current, then they will combine 
to produce a rotatory magnetic field, 
though the coil itself stands still. 
This is quite analogous to the well- 
known way in which a rotatory 
motion, without any dead points, can 
be produced from two oscillatory 
motions by using two cranks at right 
angles to one another, the impulses being given \ period 
one after the other. The above combination is called 
a di-phase system of currents. If the BB' current is 
\ period later than the AA' current, the rotation in 
Fig. 265 will be r-ight-handed. Another way of generat- 
ing a rotatory field is by a tri-phase system* (or so-called 
"dreh-strom") of currents. Let 3 alternate currents, 
differing from one another by J period (or 120°) be led 

* Tri-phase currents were used in the famous Frankfort transmission 
of power in 1891. See Art. 447. 




506 ELECTRICITY AND MAGNETISM part ii 

into the ring at the points ABC. The current flows in 
first at A (and out by B and C), then at B (flowing out 
by C and A), then at C (out by A and B), again produc- 
ing a revolving magnetic field. This is analogous to a 
3-crank engine, with the crank set at 120° apart. 

There are several ways of combining the circuits that 
receive the currents of the various phases. For example, 
the windings of Fig. 264 might be divided into four 
separate coils, each having one end joined to a common 
junction, and the four outer ends joined respectively to 
the four line wires. Or the windings of Fig. 265 might 
be arranged as three separate coils, each having one end 
joined to a common junction, and with the three outer 
ends joined respectively to the three line wires. Such 
arrangements would be called star groupings, as dis- 
tinguished from the mesh groupings of the cuts. Also 
the coils, in whichever way grouped, need not be wound 
upon a ring. The two-phase coils of Fig. 264 might be 
wound upon four inwardly-projecting pole-pieces ; and 
the three-phase coils of Fig. 265 might be wound upon 
three inwardly-projecting pole-pieces. Or in larger mul- 
tipolar machines a three-phase set of coils might be 
arranged upon a set of six, nine, twelve, or more poles, 
in regular succession. 

486. Properties of the Rotatory Field — Asynchronous 
Motors. — In such rotating magnetic fields masses of metal 
at once begin to rotate. A magnet or mass of iron, 
pivoted centrally, can take up a synchronous motion, 
but may require to be helped to start. Any pivoted 
mass of good conducting metal, such as copper, will 
also be set in motion, and will be self-starting, but 
will not be synchronous. In such a centred mass, or 
rotor, eddy-currents are set up (just as in Arago's 
rotations. Art. 457), which drag the metal mass and tend 
to turn it. The strength of these currents in the rotating 
part depends on the relative speed of the field and the 
rotor. If the rotor were to revolve with speed equal to 



CHAP. X ASYNCHRONOUS MOTORS 507 

the revolviug field, the eddy-currents would die away, 
and there would be no driving force. The rotor actually 
used in such motors consists of a cylindrical core built up 
of thin iron disks, over which is built up a sort of squirrel 
cage of copper rods joined together at their ends into a 
closed circuit. In some forms (designed by Brown) the 
rods are inserted in holes just below the surface of the 
core. The revolving part has no commutator or slip- 
rings, and is entirely disconnected from any other circuit. 
It receives its currents wholly by induction. Such 
asynchronous motors start with considerable torque (or 
turning moment) and have a high efficiency in full work. 
Similar motors for use with ordinary or single-phase 
alternate currents are now in use. To start them it is 
necessary to split the alternate current into two currents 
differing in phase. This is done by the use of a divided 
circuit, in the two branches of which different reactances 
are introduced. If in one branch there is a choking 
coil to offer inductance, the current in that branch will 
be retarded; if in the other there is a condenser, the 
current in this branch will be accelerated in phase. Com- 
bining these two currents a rotatory field is produced for 
starting the movement. When once the motor has started 
a further tm-n of the switch simply puts on the alternate 
current, as at A A' in Fig. 264, and it continues to be 
driven, though the impulse is now only oscillatory. 



CHAPTER XI 

ELECTRO-CHEMISTKY 

Lesson XL VII. — Electrolysis 

\ 487. Electromotive-force of Polarization. — The sim- 

'^' pie laws of definite chemical action due to the current 

having been laid down in Lesson XIX. it remains to 
consider the relations between the chemical energy and 
its electrical equivalent. Whenever an electrolyte is 
decomposed by a current, the resolved ions have a ten- 
dency to reunite, that tendency being commonly termed 
" chemical affinity." Thus when zinc sulphate (ZnSO^) is 
split up into Zn and SO4 the zinc tends to dissolve again 
into the solution, and so spread the potential energy of 
the system. But zinc dissolving into sulphuric acid sets 
up an electromotive-force of definite amount ; and to tear 
the zinc away from the sulphuric acid requires an electro- 
motive-force at least as great as this, and in an opposite 
direction to it. So, again, when acidulated water is 
decomposed in a voltameter, the separated hydrogen and 
oxygen tend to reunite and set up an opposing electro- 
motive-force of no less than 147 volts. This opposing 
electromotive-force, which is in fact the measure of their 
"chemical affinity," is termed the electromotive-force of 
polarization. It can be observed in any water voltameter 
(Art. 243) by simply disconnecting the wires from the 
battery and Joining them to a galvanometer, when a 
508 



CHAP. XI THEORY OF ELECTROLYSIS 509 

current Avill be observed flowing back through the volta- 
meter from the hydrogen electrode toward the oxygen 
electrode. The polarization in a voltaic cell (Art. 175) 
produces an opposing electromotive-force in a perfectly 
similar way. 

Now, since the affinity of hydrogen for oxygen is 
represented by an electromotive-force of 147 volts, it is 
clear that no cell or battery can decompose water at 
ordinary temperatures unless it has an electromotive-force 
of at least 1-47 volts. With every electrolyte there is a 
similar minimum electromotive-force necessary to produce 
complete continuous decomposition. 

488. Theory of Electrolysis. — Suppose a current to 
convey a quantity of electricity Q through a circuit in 
which there is an opposing electromotive-force E : the 
work done in moving Q units of electricity against this 
electromotive-force will be equal to E x Q. (If E and 
Q are expressed in " absolute " C.G.S. units, E x Q will 
be in ergs.) The total energy of the current, as available 
for producing heat or mechanical motion, will be dimin- 
ished by this quantity, which represents the work done 
against the electromotive-force in question. 

But we can arrive in another way at an expression for 
this same quantity of work. The quantity of electricity 
in passing through the cell will deposit a certain amount 
of metal : this amount of metal could be burned, or 
dissolved again in acid, giving up its potential energy as 
heat, and, the mechanical equivalent of heat being known, 
the equivalent quantity of work can be calculated. Q 
units of electricity will cause the deposition of Q,z grammes 
of an ion whose absolute electro-chemical equivalent 
is z. [For example, z for hydrogen is -0001038 gramme, 
being ten times the amount (see Table in Art. 240) 
deposited by one coulomb, for the coulomb is -^^ of the 
absolute C.G.S. unit of quantity.] If H represents the 
number of heat units evolved by one gramme of the sub- 
stance, when it enters into the combination in question, 



510 ELECTRICITY AND MAGNETISM part ii 

then QsH represents the value (in heat units) of the 
chemical work done by the flow of the Q units ; and this 
value can immediately be translated into ergs of work by 
multiplying by Joule's equivalent J (= 4:2 x 10®). [See 
Table on page 512.] 

We have therefore the following equality : — 

EQ = QsHJ; whence it follows that 
E = sHJ ; or, in words, the electromotioe-force of any 
chemical reaction is equal to the product of the electro-chemical 
equivalent of the separated ion into its heat of combination, ex- 
pressed in dynamical units. 

Examples.^ — (1) Electromotive-force o/ Hydrogen tending 
to unite with Oxygen. For Hydrogen z = '0001038; H 
(heat of combination of one gramme) = 34000 gramme- 
degree-units ; J = 42 X 106. 

•0001038 X 34000 X 42 X 106 = 1*48 X 108 "absolute " 
units of electromotive-force, or = 1*48 volts. 

(2) Elect)^omotive-fo)'ce of Zinc dissolving mto Sulphuric 
Acid. z = -00337 ; H = 1670 (according to Julius Thom- 
sen) ; J = 42 X lO^. 

•00337 X 1670 X 42 X 106 = 2-364 X 10^, 
or = 2-364 volts. 

(3) Electromotive-force of Copper dissolving into Sulphuric 
Acid, z = -00327 ; H = 909-5 ; J = 42 X 106. 

•00327 X 909-5 X 42 X 106 = 1-249 X 108, 
or = 1-249 volts. 

(4) Electromotive-foj^ce of a Daniell's Cell. Here zinc is 
dissolved at one pole to form zinc sulphate, the chemi- 
cal action setting up a + electromotive-force, while at 
the other pole copper is deposited by the current out of a 

* The figures given iu these examples as well as those on p. 512 for 
the heat of combination must be taken as only approximate. The heat of 
combination is different at different temperatures, and the heat evolved 
by the salt dissolving in water must also be taken into account. Exact 
figures have not yet been ascertained. In fact Von Helmholtz showed 
that the expression zHJ is incomplete, and that to it should be added a 
term BdE/dO, wherein 6 is the absolute temperature of the cell. 



CHAP. XI CONSUMPTION OF CHEMICALS 511 



solution of copper sulphate, thereby setting up an 
opposing (or — ) electromotive-force. That due to zinc 
is shown above to be + 2-3GJ: volts, that to deposited 
copper to be — 1"349. Hence the net electromotive- 
force of the cell is (neglecting the slight electromotive- 
force where the two solutions touch) 2"361 — 1-24:9 = 
I'llS volts. This is nearly what is found (Art. 181) in 
practice to be the case. It is less than will suffice to 
electrolyze water, though two Daniell's cells in series 
electrolyze water easily. 

Since 1 horse-power-hour = 746 watt-hours = 746 am- 
pere-hours at 1 volt, it follows that at Y volts the num- 
ber of ampere-hours will = 746 -=- V. Now as the weight 
of zinc consumed in a cell is 1-213 grammes per ampere- 
hour (when there is no waste) the consumption will be 
as follows : — 

Weight of zinc used [ ^ 746 ^ ^.^^o g.^^..^ i ^^^^ 
per horse-power-hour ) V V 

Hence the quantity of zinc that must be consumed to 
generate 1 horse-power-hour in any battery of cells cannot 
be less than 2 lbs. h- the available volts of a single cell of 
the battery. 

Example. — If a new cell can be invented to give 2 volts at Its terminals 
when in full work, a battery of such cells, however arranged, will 
consume 1 lb. of zinc per hour per horse-power, or 1'34 lbs. per 
"unit " of supply (or kilowatt-hour). 

An equivalent quantity of exciting and depolarizing 
chemicals will also be used, and these will increase the 
total cost per unit. It is clear that as a source of public 
supply primary batteries consuming zinc can never com- 
pete in price with dynamos driven by steam. The actual 
cost of coal to central stations in London is from 1 to 
1| pence per " unit " ; and the maximum legal price that a 
supply company may charge in Great Britain for electric 
energy is eightpence per "unit '' (see Art. 440). 

489. Electro-Chemical Power of Metals. — The ac- 
companying Table gives the electromotive-force of the 



512 



ELECTRICITY AND MAGNETISM part ii 



different metals as calculated (Art. 488) from the heat 
evolved by the combination with oxygen of a portion of 
the metal equivalent electro-chemically in amount to one 
gramme of hydrogen. The figures in the second column 
are in calories. The figures in the third column are 
calculated from these in the second by multiplying by 
the electro-chemical equivalent of hydrogen, and by 
Joule's equivalent (42 x 10^) and dividing by 10^ to 
reduce to volts. The electromotive-forces as observed (in 
dilute sulphuric acid) are added for comparison. 







E.M.r. calculated. 




Substance. 


Heat of Oxi- 
dation of 






E.M.F. 

observed. 








Equivalent. 


Eelatively 


Eelatively 






to Oxygen. 


to Zinc. 




Potassium . . . 


69,800 


3-01 


+1-1S 


+1-13 


Sodium . 




67,800 


2-91 


-fro9 




Zinc . . 




42,700 


1-83 


0- 


0- 


Iron . . 




34,120 


1-55 


-0-28 




Hydrogen 




34,000 


1-47 


-0-36 








25,100 
18,700 


1-12 


—0-71 


—0-54 


Copper . 




•80 


-1-08 


-1-047 


Silver . . 




9,000 


•39 


—1-44 




Platinum 




7,500 


•33 


-1-50 


-1-53 


Carbon . 




2,000 


•09 


-1-74 




Oxygen . 







0- 


-1-83 


-1-85 


(Nitric Acid) . . 


- 6,000 


-0-26 


-2-09 


-1-94 


(Black Oxide of 










Manganese) . . 


- 6,500 


-0-29 


2'12 


-2-23 


(Peroxide of Lead) 


-12,150 


-0-52 


-2-35 


-2-52 


(Ozone) .... 


-14,800 


-0-63 


-2-46 


-2^64 


(Permanganic 










Acid) .... 


-25,070 


-1-09 


— 2"92 


-3-03 



The order in which these metals are arranged is in 
fact nothing else than the order of oxidizability of the 
metals (in the presence of dilute sulphuric acid) ; for that 
metal tends most to oxidize which can, by oxidizing, give 
out the most energy. It also shows the order in which 



CHAP. XI LAWS OF ELECTROLYTIC ACTION 513 

the metals stand in their power to replace one another 
(in a solution containing sulphuric acid). In this order, 
too, the lowest on the list are the metals deposited first 
by an electric current from solutions containing two or 
more of them : for that metal comes down first which 
requires the least expenditure of energy to separate it 
from the elements with which it was combined. 

490. General Laws of Electrolytic Action. — In addi. 
tiou to Faraday's quantitative laws given lu Art. 240, 
the following are important : — 

(«.) Every electrolyte is decomposed into two portions, 
an anion and a kation, w^hich may be themselves either 
simple or compound. In the case of simple binary com- 
pounds, such as fused salt (NaCl), the ions are simple 
elements. In other cases the products are often compli- 
cated by secondary actions. It is even possible to deposit 
an alloy of two metals — brass for example — from a 
mixture of the cyanides of zinc and of copper. 

(h.) In binary compounds and most metallic solutions, 
the metal is deposited by the current where it leaves the 
cell, at the kathode. 

(c.) Aqueous solutions of salts of the metals of the 
alkalies and alkaline earths deposit no metal, but evolve 
hydrogen owing to secondary action of the metal upon 
the water. From strong solutions of caustic potash and 
soda Davy succeeded in obtaining metallic sodium and 
potassium, which were before unknown. If electrodes of 
mercury are employed, an amalgam of either of these 
metals is readily obtained at the kathode. The so-called 
a?7imonmm-amalgam is obtained by electrolyzing a warm, 
strong solution of sal ammoniac between mercury elec- 
trodes. 

(d.) Metals can be arranged in a definite series accord- 
ing to their electrolytic behaviour ; each metal on the list 
behaving as a kation (or being " electropositive ") when 
electrolyzed from its compound in preference to one 
lower down on the list. In such a series the oxidizable 
2 L 



514 ELECTRICITY AND MAGNETISM part n 

metals, potassium, sodium, zinc, etc., come last ; the less 
oxidizable or "electronegative" metals preceding them. 
The order varies with the nature, strength, and tempera- 
ture of the solution used. 

(e.) From a solution of mixed metallic salts the least 
electropositive metal is not deposited first, if the current 
is so strong relatively to the size of the kathode as to 
impoverish the solution in its neighbourhood. To deposit 
alloys a solution must be found in which both metals 
tend to dissolve with equal electromotive-forces. 

(/.) The liberated ions appear only at the electrodes. 

(g.) For each electrolyte a minimum electromotive-force 
is requisite, without which complete electrolysis cannot be 
effected. (See Art. 491.) 

(A.) If the current be of less electromotive-force than 
the requisite minimum, electrolysis may begin, and a 
feeble current flow at first, but no ions will be liberated, 
the current being completely stopped as soon as the 
opposing electromotive-force of polarization has risen to 
equality with that of the electrolyzing current. 

({.) There is no opposing electromotive-force of polar- 
ization when electrolysis is effected from a dissolving 
anode of the same metal that is being deposited at the 
kathode. The feeblest cell will suffice to deposit copper 
from sulphate of copper if the anode be a copper plate. 

(y.) Where the ions are gases, pressure affects the 
conditions but slightly. Under 300 atmospheres acid- 
ulated water is still electrolyzed ; but in certain cases a 
layer of acid so dense as not to conduct collects at the 
anode and stops the current. 

(k.) The chemical work done b}'" a current in an 
electrolytic cell is proportional to the minimum electro- 
motive-force of polarization. 

(/.) Although the electromotive-force of polarization 
may exceed this minimum, the work done by the current 
in overcoming this surplus electromotive-force will not 
appear as chemical work, for no more of the iou will be 



CHAP. XI HYPOTHESIS OF GROTTHUSS 515 

liberated; but it will appear as an additional quantity 
of heat (or - local heat ") developed in the electrolytic 
ceU. 

(??i.) Ohm's law holds good for electrolytic conduction. 

(«.) Amongst the secondary actions which may occur 
the following are the chief : — 

(1) The ions may themselves decompose ; as SO4 into SO3 + O. 
(2) The ions may react on the electrodes ; as when acidulated 
water is electrolj'zed between zinc electrodes, no oxygen being 
liberated, owing to the affinity of zinc for oxygen. (3) The ions 
may be liberated in an abnormal state. Thus oxygen is fre- 
quently liberated in its allotropic condition as ozone, particu- 
larly when permanganates are electrolyzed. The "nascent" 
hydrogen liberated by the electrolysis of dilute acid has pecul- 
iarly active chemical properties. So also the metals are some- 
times deposited abnormally: copper in a black pulverulent 
film ; antimony in roundish gray masses (from the terchloride 
solution) which possess a curious explosive property. When a 
solution of lead is electrolyzed a film of peroxide of lead forms 
upon the anode. If this be a plate of polished metal placed 
horizontally in the liquid beneath a platinum wire as a kathode, 
the deposit takes place in symmetrical rings of varying thick- 
ness, the thickest deposit being at the centre. These rings, 
known as Xobili's rings, exhibit all the tints of the rainbow, 
owing to interference of the waves of light occurring in the film. 
The colours form, in fact, in reversed order, the " colours of 
thin plates " of Newton's rings. 

491. Hypotheses of Grotthuss and of Clausius. — A 

complete theory of electrolysis must explain — firstly, 
the transfer of electricity, and secondly, tlie transfer 
of matter, through the liquid of the cell. The latter 
point is the one to which most attention has been 
given, since the " migration of the ions " {i.e. their trans- 
fer through the liquid) in two opposite directions, and 
their appearance at the electrodes only, are salient facts. 
The hypotliesis put forward in 1805 by Grottliuss 
serves fairly, when stated in accordance -with modern 
terms, to explain these facts. Grotthuss supposes that, 
when t.^o nulal plates at differe^it potentials are placed 



516 



ELECTRICITY AND MAGNETISM part ii 



ill a cell, the first effect produced in the liquid is that 
the molecules of the liquid arrange themselves in in- 
numerable chains, in which every molecule has its 
constituent atoms pointing in a certain direction ; the 
atom of electropositive substance being attracted toward 
the kathode, and the fellow atom of electronegative 
substance being attracted toward the anode. (This 
assumes that the constituent atoms grouped in the mole- 
cule retain their individual electric properties.) The 
diagram of Fig. 266 shows, in the case of hydrochloric 



H 



\ 




CDOSCDCDCDCDCD 



^CDiDO* 




acid, a first row of molecules distributed at random, and 
secondly grouped in a chain as described. The action 
which Grotthuss then supposes to take place is that an in- 
terchange of partners goes on between the separate atoms 
all along the line, each H atom uniting with the CI atom 
belonging to the neighbouring molecule, a + half mole- 
cule of hydrogen being liberated at the kathode, and a — 
half molecule of clilorine at the anode. This action 
would leave the molecules as in the third row, and 
would, when repeated, result in a double migration of 
hydrogen atoms in one direction and of chlorine atoms 



CHAP. XT ELECTROLYTIC CONYEXION 517 

in the other; the free atoms appearing only at the elect- 
rodes, and every atom so liberated discharging a certain 
definite minnte charge of electricity upon the electrode 
where it was liberated.* 

Clausius sought to bring the ideas of Grotthuss into 
conformity with the modern kinetic hypothesis of the 
constitution of liquids. He supposes that in the usual 
state of a liqaid the molecules are always gliding about 
amongst one another, and their constituent atoms are 
also in movement, continually separating and recombining 
into similar groups, their movements taking place in all 
possible directions throughout the liquid. But under 
the influence of an electromotive-force these actions are 
controlled in direction, so that when, in the course of the 
usual movements, an atom separates from a group it 
tends to move either toward the anode or kathode ; 
and if the electromotive-force in question be powerful 
enough to prevent recombination, these atoms will be 
permanently separated, and will accumulate around the 
electrodes. This theory has the advantage of account- 
ing for a fact easily observed, that an electromotive-force 
less than the minimum which is needed to effect com- 
plete electrolysis may send a feeble current through an 
electrolyte for a limited time, until the opposing electro- 
motive-force has reached an equal value. Von Helmholtz, 
who gave the name of electrolytic convexion to this pheno- 
menon of partial electrolysis, assumed that it takes place 
by the agency of uncombined atoms previously existing 
in the liquid. 

* Mr. G. J. Stoney has reckoned, from considerations founded on 
the size of atoms (as calculated by Loschmidt and Lord Kelvin), that 
for every chemical bond ruptured, a charge of 10—20 of a coulomb is 
transferred. [E. Budde says 17 x 10—20 coulomb.] This quantity would 
appear therefore to be the natural atomic charge or unit. To tear one 
atom of hydrogen from a hydrogen compound this amount of electricity 
must be sent through it. To liberate an atom of zinc, or any other diva- 
lent metal from its compound, implies the transfer of twice this amount 
of electricity. 



518 



ELECTRICITY AND MAGNETISM part 



Lessox XLVIII. — Accumulators 



492. Accumulators or Secondary Batteries. — A 

voltameter, or series of voltameters, whose electrodes 
are thus charged respectively with hydrogen and oxygen, 
will serve as secondary batteries, in 
which the energy of a current 
may be stored up and again given 
out. Ritter, who in 1803 con- 
structed a secondary pile, used 
electrodes of platinum.. It will 
be seen that such cells do not 
accumulate or store electricity; 
what they accumulate is energy, 
which they store in the form of 
chemical work. A secondary cell 
resembles a Leyden jar in that 
it can be charged and then dis- 
charged. The residual charges of 
Le3'den jars, though small in 
quantity and transient in their 
discharge, yet exactly resemble 
the polarization-charges of volta- 
meters. Yarley found 1 sq. cen- 
tim. of platinum foil in dilute 
acid to act as a condenser of 
about 63 microfarads capacity, 
when polarized to a potential- 
difference of 1 volt. Gaston Plante. in 1860, devised a 
secondary cell consisting of two pieces of sheet lead 
rolled up (without actual contact) as electrodes, dipping 
into dilute sulphuric acid, as in Fig, 267. 'J'o " form " 
or prepare the lead it was charged with currents which 
after a time were reversed in direction, and after a further 
time again reversed until, after several reversals, it became 
coated with a semi-porous film of brown dioxide of lead 




Fis-. 267. 



CHAP. XI 



ACCUMULATORS 



519 



on the anode plate ; the kathode plate assuming a spongy 
metallic state presenting a large amount of surface of 
high chemical activity. When such a secondary battery, 
or accumulator, is charged by connecting it with a dynamo 
(shunt-wouud), or other powerful generator of currents, 
the anode plate becomes peroxidized, while the kathode 
plate is deoxidized by the hydrogen that is liberated. 
The plates may remain for many days in this condition, 
and will furnish a current until the two lead surfaces 
are reduced to a chemically inactive state. The electro- 
motive-force of such cells is from 2-0 to 1-85 volts during 
discharge. Plante ingeniously arranged batteries of such 
cells so that they can be charged in parallel, and dis- 
charged in series, giving (for a short time) strong currents 
at extremely high voltages. Faure, in 1881, modified 
the Plante accumulator by giving the two lead plates a 
preliminary coating of red-lead (or minium). When a 
current is passed through the cell to charge it, the red- 
lead is peroxidized at the anode, and reduced, — first to a 
condition of lower oxide, 
then to the spongy metallic 
state, — at the kathode, and 
thus a greater thickness of 
the working substance is 
provided, and takes far 
less time to "form" than 
is the case in Plante's cells. 
In modern accumulators 
the red-lead (or litharge), 
freshly mixed with dilute 
sulphuric acid to the form 
of a paste, is pressed into 
the holes of a leaden grid, 
shaped so as to give it a 
good mechanical attachment, 
process of "formation" the hardened paste is reduced 
on one plate and peroxidized on the other. A cell of the 




Fig. 2(i6. 



During the subsequent 



520 ELECTRICITY AND MAGNETISM part u 

kind known as the E.P.S. cell is shown in Fig. 268. 
Accumulators are still made on the Plante method from 
metallic lead, which is first finely divided on its sur- 
face by some mechanical or chemical means, and then 
" formed " by prolonged charging. Cells of this type are 
not so subject to disintegration as paste cells, and may be 
discharged at a greater rate. To keep accumulators in 
good condition they should be charged up every day till 
full (known by bubbles rising) and not be discharged too 
quickly. The density of acid should never be allowed 
to exceed 1-21 nor fall below 1*15. 

493. Grove's Gas Battery. — Sir W. Grove devised a 
cell in which platinum electrodes, in contact respectively 
with hydrogen and oxygen gas, replaced the usual zinc 
and copper plates. Each of these gases is partially 
occluded by the metal platinum, which, when so treated, 
behaves like a different metal. 

Attempts have been made to generate electricity on 
a larger scale b}^ means of gas batteries. Mond and 
Langer found that the gTeatest E.M.F. to be obtained 
from a cell of hydrogen and oxygen, with finely divided 
platinum as collectors, w^as 0-97, the difference between 
this and the theoretical, 147, being lost in heat generated 
by the condensation of the gases by the platinum. 

Lesson XLIX. — Electrodeposition 

494. Electrometallurgy. — The applications of electro- 
chemistry to the industries are threefold. Firstly, to the 
reduction of metals from solutions of their ores, the pro- 
cess is useful in the accurate assay of certain ores, as, for 
example, of copper; secondh/, to the copying of types, 
plaster casts, and metal-work by kathode deposits of 
metal ; thirdly, to the covering of objects made of baser 
metal with a thin film of another metal, such as gold, 
silver, or nickel. All these operations are included under 
\^\iQ general term of electrometallurgy. 



CHAP. XI ELECTROTYPING 521 

It is not established whether the reduction of aluminium 
in the electric f arnace is partly electrolytic or whether it 
is purely che-mical, but the process may be mentioned 
here. Aluminium oxide is mixed with charcoal and 
placed between the ends of two thick carbon rods in a 
closed firebrick furnace lined with charcoal. A current 
of several thousand amperes is passed between the carbon 
rods and the aluminium ore is melted and parts with its 
oxygen to carbon. The liberated aluminium is commonly 
allowed to alloy with some other metal, such as copper, 
previously added to the charge, and forms the famous 
aluminium bronze. Pure aluminium is now produced in 
large quantities by the electrolysis of fused cryolite, 
which is a double fluoride of aluminium and sodium. 

Copper of a high degree of purity is produced on a 
large scale by suspending anodes of impure copper in a 
solution of copper sulphate and electrolytically depositing 
piu-e copper on the kathodes. The impurities such as 
arsenic being more electronegative than copper are left 
in the bath. 

495. Electrotyping. — In 1836 De La Rue observed 
that in a Daniell's cell the copper deposited out of the 
solution upon the copper plate which served as a kathode 
took the exact impress of the plate, even to the scratches 
upon it. In 1839 Jacobi in St. Petersburg, Spencer in 
Liverpool, and Jordan in London, independently devel- 
oped out of this fact a method of obtaining, by the 
electrolysis of copper, impressions (in reversed relief) of 
coins, stereotype plates, and ornaments. A further im- 
provement, due to Murray, was the employment of 
moulds of plaster or wax, coated with a film of plumbago 
in order to provide a conducting surface upon which the 
deposit could be made. Bronze in the form of a fine 
powder is much used instead of jjlumbago, being a better 
conductor. Jacobi gave to the process the name of galvano- 
plasdc, a term generally abandoned in favour of the term 
electrotyping or electrotype process. 



522 ELECTRICITY AXD MAGXETISM part ii 

Electrotypes of copper are easily made by hanging a 
suitable mould in a cell containing a nearly saturated and 
slightly acidulated solution of sulphate of copper, and 
passing a current of a battery through the cell, the mould 
metallized on its surface being the kathode, a plate of 
copper being employed as an anode, dissolving gradually 
into the liquid at a rate exactly equal to the rate of 
deposition at the kathode. This use of a separate cell or 
" bath " is more convenient than producing the electro- 
types in the actual cell of a Daniell's batteiy. The 
process is largely employed at the present day to repro- 
duce repousse and chased ornament and other works of 
art in facsimile, and to multiply copies of wood blocks for 
printing. Almost all the illustrations in this book, for 
example, are printed from electrotype copies, and not 
from the original wood blocks, which would not wear so 
weU. In all deposition processes success largely depends 
on having the proper current-density. To deposit metals 
that are more positive than hydrogen, such as zinc or 
chromium, it is advisable to use concentrated solutions 
and high current-densities. For metals that are less 
positive, such as cop)per and silver, the current-density 
may be less. To procure a good tough deposit of copper 
the current should not exceed 15 amperes per square foot 
of kathode surface. If a more rapid deposit is i-equired, 
a solution of nitrate of copper should be used and kept in 
rapid agitation. 

To deposit iron (by the process known as acierage, or 
steel-facing) a very large sheet of iron is used as anode, 
and the liquid used is simply a solution of sal ammoniac 
in water. This solution is '• charged " with iron by 
passing the cmTent for a little time through the bath 
prior to inserting the object to be steel-faced. 

496. Electroplating. — In 1801 WoUaston observed 
that a piece of silver, connected with a more positive 
metal, became coated with copper when put into a solu- 
tion of copper. In 1805 Brugnatelli gilded two silver 



ELECTROPLATING 



52J 



medals by making them the kathodes of a cell containing 
a solution of gold. Messrs. Elkington, about the year 
ISJrO, introduced the commercial processes of electro- 
plating. In these processes a baser m.etal, such as German 
silver (an alloy of zinc, copper, and nickel), is covered 
with a thin film of silver or gold, the solutions employed 
being, for electro-gilding, the double cyanide of gold and 
potassium, and for electro-silcering the double cyanide of 
silver and potassium. 

Fig. 269 shows a battery and a plating-vat containing 
the silver solution. As anode is hung a plate of metallic 




Fijr. 26[). 



silver which dissolves into the liquid. To the kathode 
are suspended the spoons, forks, or other articles which 
are to receive a coating of silver. The addition of a 
minute trace of bisulphide of carbon to the solution 
causes the deposited metal to have a bright surface. If 
the current is too strong, and the deposition too rapid, 
the deposited metal is grayish and crystalline. 

In gilding base metals, such as pewter, they are 
usually first copper-coated. The gilding of the insides of 
jugs and cups is effected by filling the jug or cup with the 
gilding solution, and suspending in it an anode of gold. 



524 ELECTRICITY AND MAGNETISM paet ii 

the vessel itself being connected to the — pole of the 
batten\ 

In silvering or gilding objects of iron it is usual first 
to plate them with a thin coating of copper deposited 
from an "alkaline" copper bath containing an ammonia- 
cal solution of cyanide of copper. Brass is deposited also 
from an ammoniacal solution of the mixed cyanides of 
copper and zinc. In the deposition of nickel a solution 
of the double sulphate of nickel and ammonium is used ; 
the anode being a sheet of rolled (or cast) nickel. 

Except on the ver}^ small scale batteries are now 
seldom used for electrotyping and plating. A shunt- 
wound dynamo designed to give a large output of current 
at 5 to 10 volts pressure is generally preferred. 

496a. Other Electrolytic Processes. — The electro- 
lytic action of the current is now commercially employed 
for other purposes than the deposition of metals. By the 
electrolysis of chloride of potassium under suitable con- 
ditions chlorate of potash is now manufactured in large 
quantities. Bleaching liquors containing hypochlorites 
can also be produced from chlorides. Caustic soda is 
prepared by electrolysis of common salt; and several 
electrolytic methods of disinfecting sewage have been 
proposed. 

It has also been shown that the slow processes of tan- 
ning can be accelerated by the aid of electric currents, the 
action being probably osmotic rather than electrolytic. 

It seems probable that in the future the use of electric 
currents will enter largely into the chemical manufactures. 



CHAPTER Xir 

TELEGKAPHY 

Lesson L. — Electric Telegraphs 

497. The Electric Telegraph. — It is difficult to 
assign the invention of the telegraph to any particular 
inventor. Lesage (Geneva, 1774), Lomond (Paris, 1787), 
and Sir F. Ronalds (London, 1816) invented systems for 
transmitting signals through wires by observing at one 
end the divergence of a pair of pith-balls when a charge 
of electricity was sent into the other end. Cavallo 
(London, 1795) transmitted sparks from Leyden jars 
through wires " according to a settled plan." Soemmering 
(Munich, 1808) established a telegraph in which the 
signals were made by the decomposition of water in volta- 
meters ; and the transmission of signals by the chemical 
decomposition of substances was attempted by Coxe, R. 
Smith, Bain, and others. Ampere (Paris, 1821) suggested 
that a galvanometer placed at a distant point of a circuit 
might serve for the transmission of signals. Schilling 
and Weber (Gottingen, 1833) employed the deflexions of 
a galvanometer needle moving to right or left to signal an 
alphabetic code of letters upon a single circuit. Cooke 
and Wheatstone (London, 1837) brought into practical 
application the first form of their needle telegraph. Henry 
(New York, 1831) utilized the attraction of an electro- 
magnet to transmit signals, the movement of the armature 
525 



526 ELECTRICITY AND MAGNETISM part ii 

producing audible sounds according to a certain code. 
]\Iorse (New York, 1837) devised a telegraph in which 
the attraction of an armature by an electromagnet was 
made to mark a dot or a dash upon a moving strip of 
paper. Steinheil (Munich, 1837) discovered that instead 
of a return-wire the earth might be used, contact being- 
made to earth at the two ends by means of earth-plates 
(see Fig. 274) sunk in the ground. Gintl (1853) and 
Stearns (Xew York, 1870) devised methods of duplex 
signalling. Stark (Vienna) and Bosscha (Leyden, 1855) 
invented diplex signalling, and Heaviside (London, 1873} 
and Edison (Newark, N. J., 1871) invented quadruplex 
telegraphy. Yarley (London, 1870) and Elisha Gray 
(Chicago, 1874) devised harmonic telegraphs. For fast- 
speed work AYheatstone devised his automatic transmitter, 
in which the signs which represent the letters are hrst 
punched by machinery on strips of i)aper; these are then 
run at a great speed through the transmitting instrument, 
which telegraphs them off at a nmch greater rate than if 
the separate signals Avere telegraphed by hand. Hughes 
devised a type-printing telegraph. Wheatstone invented 
an ABC telegraph in which signals are spelled by a hand 
which moves over a dial. Cowper (1876) and Elisha 
Gray (1893) invented autographic writing telegraphs. 
For cable-working Lord Kelvin invented his mirror 
galvanometer and his delicate siphon-recorder. It is 
impossible in these Lessons to describe more than one or 
two of the simple ordinary forms of telegraph instrument 
now in use in Great Britain. Students desiring further 
information should consult the excellent manuals on 
Telegraphy by Messrs. Preece and Sivewright, and by 
.Mr. Culley. 

498. Single-Needle Instrument. — The single-needle 
instrument (Fig. 270) consists essentially of a vertical 
galvanometer, in which a lightly hung magnetic needle 
is deflected to right or left when a current is sent, in 
one direction or the other, around a coil surrounding" 



CHAP. XII SIXGLE-NEEDLE TELEGRAPH 



527 



the needle ; the needle visible in front of the dial is but 
an index, the real magnetic needle being behind. A code 
of movements agTeed upon 
comprises the whole alphabet 
in combinations of motions 
to right or left. In order to 
send currents in either direc- 
tion through the circuit, a 
'' signalling key " or '• tap- 
per" is usually employed. 
The tapper at one end of 
the line works the instru- 
ment at the other; but for 
the sake of convenience it 
is fixed to the receiving in- 
strument. In Fig. 270 the 
two protruding levers at the 
base form the tapper, and 
by depressing the right hand one or the left hand one, 
currents are sent in either direction at will. 

The principle of action will be made more clear by 




Fig. 270. 




reference to Fig. 271, which shows a separate signalling 
key. The two horizontal levers are respectively in com- 
munication with the "line,'' and with the return-line 



1'^ 



528 ELECTRICITY AND MAGNETISM part ii 

through "earth." When not in use both levers spring- 
up against a cross strip of metal joined to the zinc pole 
of the battery. At their further end is another cross 
strip, which communicates with the copper (or +) pole 
of the battery. On depressing the "line" key the 
current runs through the line and back by earth, or in 
the positive direction. On depressing the " earth " key 
(the line-key remaining in contact with the zinc-connected 
strip), the current runs through the earth and back by 
the line, or in the negative direction. Telegraphists 
ordinarily speak of these as positive and negative currents 
respectively. 

499. The Morse Instrument. — The most widely 
used instrument at the present day is the Morse. It 
consists essentially of an electromagnet, which, when a 
current passes through its coils, draws down an armature 
for a short or a long time. It may either be arranged as 
a " sounder," in which case the operator who is receiving 
the message listens to the clicks, and notices whether the 
intervals between them are long or short ; or it may be 

arranged as an 
" embosser" to print 
dots and dashes 
upon a strip of 
paper drawn by 
clockwork through 
the instrument. In 
the most modern 
foi'm, however, the 
Morse instrument 
is arranged as an 
^^"- -'^'^- " ink -writer " in 

w^hich the attraction of the armatm^e downwards lifts a 
little inky wheel and pushes it against a ribbon of paper. 
The Morse Sounder, which is almost universal in the 
United States, and is being increasingly used in the 
British Telegraph Service, is depicted in Fig. 272. In 




CHAP. XII 



MORSE INSTRUMENT 



529 



this instrument the electromagnet is of inverted horse- 
shoe pattern, having the coils wound on two bobbins 
which are slipped over vertical cores. Above the poles lies 
an iron armature fixed across the pivoted lever. When- 
ever the current passes thi-ough the coils the armature is 
attracted down, and the lever makes a click as it strikes 
against a stop. As soon as the cuiTent ceases the lever is 
raised by a spring and strikes against a top stop. There 
are therefore two clicks heard. When a "dot" is sig- 
nalled the two clicks are heard immediately after one 
another. AVhen a "dash" is signalled the interval be- 
tween the clicks is longer. With a little practice it 
becomes easy to read the sounder. 

The :\rorse Ink- Writer, as used in the British Postal 
Telegi-aph Service, is depicted in Fig. 273. A piece of 
clockwork causes a ribbon of paper (coiled up in the 



Local Battery 




l^]HH<^'^'^H'^'^•^l-i 



Earth 



Sending Battery 

Fig. 273. 



base of the instrument) to be slowly drawn between 
rollers, while the dots and dashes are printed on it by 
the ink-wheel affixed to the end of the lever. A momen- 

2 M 



530 ELECTKlCIXr AND MAGNETISM part ii 

tary current prints a mere dot; but if the current con- 
tinues to flow for a longer time while the ribbon of paper 
moves on, the ink-wheel records a dash. The connexions 
show how the instrument is worked by a local battery 
and a relay. 

499a. The Morse Alphabets. — The international 
Morse code, or alphabet of dots and dashes, is as 
follows : — 



A .— 


J . 


S 


B — . . . 


K — .— 


T 


C — . — . 


L . — . . 


U 


D — . . 


M 


Y 


E . 


X — . 


W 


F . . — . 





X 


G . 


p . . 


y 


H 


Q .- 


z 


I .. 


R . — . 





The American Morse code, originated by Morse himself, is 
used only in tlie United States and Canada. It differs in many 
respects from the International code, the signals for some of the 
letters depending on the length of the spacings between the dots 
and dashes ; and more than four marks are used to form some 
of the letters. The marks for H, Y, and Z are four dots, but 
they are differently spaced. The following is the American 
Morse code : — 



A .— 


M 


Y . . . . 


B — . . . 


N — . 


Z . ... 


C .. . 


. . 


1 . 


D — . . 


P ..... 


2 .. — .. 


E . 


Q ..-. 


3 ... — . 


F . — . 


R . . . 


4 — 


G . 


S ... 


5 


H 


T — 


6 


I . . 


U ..- 


7 . 


J — . — . 


Y . . . — 


8 — 


K — .— 


^V . 


9 — . .- 


L 


X . — . . 






CHAP. XH 



MORSE KEY 



531 



499b. The Morse Key. — ■ The key used for operat- 
ing Morse telegraphs. The American pattern diit'ers 
someAvhat from the European pattern, and the mode of 
use is not precisely the same. 

The general apj)earance of the American pattern of 
Zdorse key is shown in Fi"-. 274:. 




Vvj:. 274. 



The key is fastened to the table by the screws B and 
L, the former being insulated from the metal base and 
leyer, while L is not insulated. One wire is clamped 
to the metal of the key at L, the other is clamped to B. 
The leyer, which is provided with a finger-piece, has on 
its lower side a short platinum pin just above the head 
of the screw B, so that when the operator depresses the 
lever it makes contact on the head of the screw and com- 
pletes the circuit from B to L. The range of motion 
allowed the lever is regulated by a screw-stop in the 
further end of the lever. Beside the parts named the key 
is usually provided with a switch, shown in the Fig. 274 
with a small vertical handle. When this is moved to the 
left it short-circuits the key, and puts B into direct con- 
nexion with L. When moved to the right, the circuit is 
open until such time as the lever is depressed. 

The Morse key as used in the British telegraphs is 



632 



ELECTRICITY AND MAGNETISM part ii 




Fig. 27 



depicted in Fig. 275. The line wire is connected with 

the central pivot A. 
A spring keeps the 
front end of the key 
elevated when not 
in use, so that the 
line wire is in com- 
munication through 
the rear end of the 
key with the receiv- 
ing instrument or 
relay. Depressing 
the key breaks this communication, and by putting the 
line wh-e in communication with the sending battery 
transmits a current through the line. 

500. Open and Closed Circuit Working. — Em'opean 
telegraphs work on the open-circuit plan, the battery being 
out of circuit when no message is being sent. American 
telegraphs are usually on the closed-circuit plan, the 
current being always on until interrupted to send signals. 
Each plan has its advantages. The closed-circuit plan 
enables a way-line to unite a number of isolated stations 
all in a single circuit, each one of which can signal to all 
the rest by opening the circuit. Further, any failure in 
the line immediately reports itself by the stoppage of the 
current. The open-circuit plan, which is better suited 
for communication among dense populations, and for all 
lines where no instruments are wanted to be inserted at 
intermediate points, has the advantage of only using the 
batteries when the telegraph is in actual use. 

In the open-circuit plan the key acts, as previously 
described, merely to open or close the circuit. The 
general arrangement of apparatus at an intermediate or 
" way " station is shown in Fig. 276. The current com- 
ing along the line enters by the line wire on the right 
and comes in to the metal base of the key K, where it 
finds a passage along the switch G (which is closed) to 



CHAP. XII 



OPEN-CIRCUIT METHOD 



533 



the head H of the screw (described as screw B of Fig. 
274). Thence it passes to the relay R, entering it at the 
terminal A, passing around the electromagnet M of the 
relay ; and issuing by the terminal B it passes down 




Fisr. 2T6. 



the line to the next station. This current is furnished 
either by a single battery inserted in the line, or by two 
batteries, one at each end of the line acting in the same 
direction. The action of the relay is considered below. 
In the open-circuit method, as it is necessary that a 
line should be capable of being worked from either end, 
a battery is used at each, and the wires so connected that 
when at either end a message is being received, the 
battery circuit at that end shall be open. Fig. 277 shows 
the simplest possible case of such an arrangement. At 
each end is a battery 2c, one pole of which is put to earth, 
and the other communicates with the middle point of a 
Morse key K. This key is arranged (like that in Fig. 
275) so that when it is depressed to send a signal through 
the line it quits contact with the receiving instrument at 



634 



ELECTRICITY AND MAGNETISM part n 



its own end. Both ends of the lever must therefore be 
furnished with contact-pins of platinum ; and the key 
acts as a two-way key. The cm-rent flowing through the 




Fig. 277. 

line passes through K' and enters a receiving instrument 
G' at the distant end, where it produces a signal, and 
returns by the earth to the battery whence it started. A 
similar battery and key at the distant end suSice to trans- 
mit signals in the opposite direction to G when K is not 
depressed. The diagram is drawn as if G were a simple 
galvanometer ; but the arrangement would perfectl}^ suit 
the Morse instrument, in which it is only required at 
either end to send long and short currents without revers- 
ing the direction, as with the needle instruments. In 
this diagram the battery current is never reversed 
and the method is known as a sincjle-current method. 
There is a so-called double-current method of working, in 
which reversing keys (resembling the tapper of Fig. 
271) are used to send after each current in the positive 
direction a second current in the negative direction. The 
double-current method has the advantasfe of enabling 



CiiAP. xii RELAYS 



the sigiiaUiiig to be more rapid on long lines when the 
retardation due to the static charging of the line is of 
importance. The second current helps to curb the first 
and makes the signals shorter and sharper. 

501. Relays. — In working over long lines, or where 
there are a number of instruments on one circuit, the 
currents are often not strong enough to work the record- 
ing instrument directly. In such a case there is inter- 
posed a relay or repeater. This instrument consists of 
an electromagnet round which the line current flows, and 
whose delicately poised armature, when attracted, makes 
contact for a local circuit in which a local battery and 
the receiving Morse instrument (sounder, or writer) are 
mcluded. The principle of the relay is, then, that a cur- 
rent too weak to do the work itself may set a strong local 
cmTent to do its work for it. 

In the American plan of working (Fig. 276), the relay 
is a simple electromagnet having a soft-iron core, and an 
armature of iron which it attracts whenever a current 
flows round its coils. It pulls its armature no matter 
which way the current flows. Such a non-polarized 
relay of the Western Union pattern is depicted in Fig. 




Fig. 278. 



278. Its mode of operation is explained by the dia- 
grammatic plan of Fig. 270. Here M is the electromag- 
net, with its iron armature lightly pivoted at P, and 
controlled by the spring V. When any current passes, iL^i 



ELECTRICITY AND MAGNETISM part ii 



light lever or tongue on which the armatui'e is mounted 
turns on its pivot P, and makes contact against the stop D, 
thereby closing a local circuit DXLSYP. which includes 
the sounder S and a local battery L. 

In the closed-circuit method of working, and in 
duplex telegraphy " polarized relays " are used, which 
will respond to currents flowing in one du^ection only. 
The polarized relay of Siemens's pattern is shown in 
diagTam in Fig. 279. In it a permanently magnetized 
steel magnet is employed to produce an initial magnetism 
in the cores of the electromagnet, and in the pivoted 
lever or tongue. The magnet has its S pole bent up at 





<7 TO LINE 

/ 






s 


^'---v-v 


n 


\) 


TO LOCAL / 
BATTERY I 


VJb' 


) 


s 


pb T^ 

SOUNDER 


^i 


3 LINE 







Fig. 2T9. 

right angles and divided so that the tong-ue «D of the 
relay, which is of iron, may be thereby polarized or 
given a south polarity. Attached to the X pole of the 
magnet are the two cores, over which the two bobbins 
are slipped, these cores ending in the two pole-pieces 
marked rz, n', which are of northern polarity. They both 
attract the tongue that lies between them, the nearer one 
pulling more strongly. If now a current circulates round 
the coils it will tend to strengthen one of the poles and 
weaken the other. If it flows in such a direction as to 
stren'>-tlien n and weaken n' . the tongue will be attracted 



CHAP. XII 



RELAYS 



537 



over and will make contact against the stop which is in 
connexion with the local battery, and so will work the 
sounder. K the current flows iu the opposite sense, so 
as to weaken n and strengthen n', the tongue will tend to 
move the other way and will make no signal. Even 
when there is no current the tongue returns back, being- 
attracted to the nearer pole-piece. Xo springs are 
necessary. 

The sensitive form of polarized relay adopted in the 
British Postal Telegraphs, is shown in Fig. 280. Here the 
tongue of the relay is fixed 
on a vertical spindle, piv- 
oted in jewelled holes, 
which has two short iron 
projections upon it. This 
spindle is polarized by a 
powerful steel magnet of 
compact shape. The two 
projections lie between a 
pair of upper and a pair 
of lower pole-pieces upon 
the two vertical u'on cores 
of the electromagnets. 
These are wound with coils 
of exceedingly fine silk- 
covered wire. The con- 
nexions are indicated in Fig. 273 where the tongue of the 
relay is shown to make circuit, when it touches the stojD, 
for a local battery and the Morse ink-writer. Whenever 
a current comes in the right direction in the line it causes 
the tongue of the relay to close the local circuit, and 
causes the Morse to record either a dot or a dash on the 
strip of paper. 

502. Faults in Telegraph Lines. — Faults may occur 
iu telegraph lines from several causes ; either from the 
breakage of the wires or conductors, or f i-om the break- 
age of the insulators, therebv short-circuiting the current 




Fi^. 280. 



538 ELECTRICITY AND MAGNETISM part ii 

through the earth before it reaches the distant station, 
or, as in overhead wires, by two conducting wires touch- 
ing one another. Various modes for testing the existence 
and position of faults are known to telegraph engineers; 
they depend upon accurate measurements of i-esistance or 
of capacity. Thus, if a telegraph cable part in mid-ocean 
it is possible to calculate the distance from the shore end 
to the broken end by comparing the resistance that the 
cable is known to offer per mile with the resistance 
offered by the length up to the fault, and dividing the 
latter by the former. 

503. Duplex and Quadniplex Telegraphy. — To send 
two messages through one wire, one from each end, at 
the same time, is known as duplex working. There are 
two distinct methods of arranging apparatus for duplex 
working. The first of these, known as the differential 
method, involves the use of instruments wound with dif- 
ferential coils, and is applicable to special cases. The 
second method of duplex working, known as the bridge 
method, is capable of much more general application. The 
diagram of Fig. 281 will explain the general principle. 
The first requirement in duplex working is that the 
instrument at each end shall only move in response to 
signals from the other end, so that an operator at R may 
be able to signal to the distant instrument M' without his 
own instrument M being affected, M being all the while 
in circuit and able to receive signals from the distant 
operator at W . To accomplish this the circuit is divided 
at R into two branches, which go, by A and B respectively, 
the one to the line, the other through a certain resistance 
P to the earth. If the ratio between the resistances in 
the arms RA and KB is equal to the ratio of the resistances 
of the line and of P, then, by the principle of Whea-tstone's 
Bridge, no current will pass through M. So M does not 
show any currents sent from R; but M' will show them, 
for the current on arriving at C will divide into two 
parts, part flowing round to the earth by R', the other 



CHAP. XII 



DUPLEX TELEGRAPHY 



539 



part flowing through M' and producing a signal. If, 
while this is going on, the operator at the distant R' 
depresses his key and sends an equal current in the 




Fig. 281. 

opposite direction, the flow through the line will cease ; 
but M will now show a signal, because, although no 
current flows through the line, the current in the branch 
RA will now flow down through M, as if it had come 
from the distant R', so, whether the operator at R be 
signalling or not, M will respond to signals sent from R'. 
In duplexing long lines and cables condensers are em- 
ployed in the arms RA and RB of the bridge; and 
instead of a mere balancing resistance at P and Q there 
is used an "artificial cable," a combination of condensers 
and resistances to imitate the electrical properties of the 
actual line or cable between the stations. 

The Diplex method of working consists in sending 
two messages at once through a wire in the same direc- 
tion. To do this it is needful to employ one set of instru- 
ments which works only with currents in one given 
direction, and a second set which works only when the 
current, in either direction, exceeds a certain strength. 
The method involves the use of polarized relays, which, 
being themselves permanently magnetized, respond there- 
fore only to currents in one direction, and of set-up non- 
polarized relays which will not respond to currents below 
a certain minimum. Two keys are used ; one reversing 
the current and sending it in either positive or negative 
direction, the other sending current always in the same 



540 



ELECTRICITY AND MAGNETISM part ii 



direction, but sometimes weak, sometimes strong. One 
key controls the direction, the other the strength of the 
current. 

The method used by Edison for transmitting is shown 
in Fig. 282. In the position shown the battery B has its 

terminals at ^N" and P; the 






- ^■ 



^ 



mu 



Wl 



3 



-H|l|l|l|l| 
B' 

Fig. 282. 



^^^ current passing from B 

L- through Kg 'to the spring S, 

and thence to P. If the key 
K' is worked, the currents 
flow into or out of the line, 
and, if a polarized relay is 
inserted at the distant re- 
ceiving station, it will work 
its sounder only for currents 
Kj in one direction, as sent by 

K', no matter wliether these 
currents are strong or weak. 

1 1 ' — 1 1 1 1 1 1 1 1 1 1 1 1 ' As shown in the figure, the 

second battery B', which 
has more cells than B, is on 
open circuit. If, however, 
Kg be depressed, the spring S comes into contact with the 
point m and breaks contact with n, so that now the entire 
range of battery is thrown into operation. Whenever 
Kg is depressed, therefore, the points N and P retain their 
polarity, but the current is of three or four times its 
original strength. All contacts are made by springs 
properly adjusted so that Kg never breaks the circuit in 
producing the change of strength of current. The mes- 
sage transmitted by Kg is received on a non-polarized 
relay, the tongue of which is controlled by a spring so 
adjusted that the weak currents of battery B will not 
cause the electromagnets to pull over the armature ; but 
when Kg is worked, the current due to B + B' easily pulls 
the armature over. 

The Quadmplex method of working combines the 



CHAP. XII SUBMARINE CABLES 541 

duplex and the diplex methods. On one and the same 
line are used two sets of receiving instruments, one of 
which (^vorked by a polarized relay) works only when 
the direction of the current is changed, the other of which 
(worked by a non-polarized relay adjusted with springs 
to move only with a certain minimum force) works only 
when the strength of the current is changed and is inde- 
pendent of their direction. If in Fig. 281, the diplex 
transmitting apparatus just described were inserted at 
each end instead of the two keys R and R', and if between 
A and B were placed in series the two relays, the figure 
would represent the general arrangement of the quadru- 
plex system as used widely in the United States. 



Lesson LI. — Cable Telegraphy 

504. Submarine Cables. — Telegraphic communica- 
tion between two countries separated by a strait or ocean 
is carried on through cables sunk to the bottom of the 





Fig. 2S3. 

sea, which carry conducting wires carefully protected by 
an outer sheath of insulating and protecting materials. 
The conductor is usually of purest copper wire, weighing 
from 70 to 400 lbs. per nautical mile, made in a seven- 
fold strand to lessen risk of breaking. Figs. 283 and 
284 show, in then- natural size, sections of the Atlantic 



I 



542 ELECTRICITY AND MAGNETISM part ii 

caliles laid in 1857 and 1836 respectively. In the latter 
cable, which is of the usual type of cable for long lines, 
the core is protected first by a stout layer of guttapercha, 
then by a woven coating of jute, and outside all an 
external sheath made of ten iron wires, each covered 
with hemp. The shore ends are even more strongly pro- 
tected by external wires. 

505. Speed of Signalling through Cables. — Signals 
transmitted through long cables are retarded, the re- 
tardation being due to two causes. 

Firstly. The self-induction of the cu-cuit prevents the 
current from rising at once to its height, the retardation 
being expressed by Helniholtz's equation (Art. 460). 

Secondli/, The cable in its insulating sheath, when 
immersed in water, acts laterally like a Lej'den jar of 
enormous capacity (as explained in Art. 274), and the 
first portions of the current, instead of flowing through, 
remain in the cable as an electrostatic charge on the sur- 
face of the guttapercha. For every separate signal the 
cable must be at least partially charged and then dis- 
charged. CuUey states that when a current is sent 
through an Atlantic cable from Ireland to Xewfoundland 
no effect is produced on the most delicate instrument at 
the receiving end for two-tenths of a second, and that it 
requires three seconds for the current to gain its full 
strength, rising in an electric wave which travels forward 
through the cable. The strength of the current falls 
gTadualh' also when the circuit is broken. The greater 
part of this retardation is due to electrostatic charge, not 
to electromagnetic self-induction. The time required to 
transmit a given number of signals varies in proportion 
both to K the capacity and II the resistance of the cable : 
it is therefore proportional to KR, and as each of these 
quantities is proportional to the length of the cable, it 
follows that the retardation is proportional to the square 
of the length of the cable. The various means adopted 
to get rid of this retardation are explained in Art. 323. 



ciiAP. XII MULTIPLEX TELEGRAPHS 543 

It is usual to insert iu the circuit at eacli eud of the cable 
a condenser of several microfarads, through which the sig- 
nals pass. The tendency of the condenser to discharge 
helps to CLirh the signals and make each shorter and 
sharper. It is theoretically possible (compare Art. 438) 
to compensate capacity by self-induction; but as the 
capacity of a cable is lateral, not longitudinal, and dis- 
tributed all along it, the self-induction coils to compen- 
sate the retardation would have to be applied as shunts 
at intervals. A cable with a self -inductive shunt or leak, 
at a point near its middle transmits signals more rapidly 
than one not so compensated. 

506. Receiving Instruments for Cables. — The mirror- 
galvanometer of Lord Kelvin (Art. 215) was devised 
for cable signalling, the movements of tlie spot of light 
sweeping over the scale to a short or a long distance 
sufficing to signal the dots and dashes of the Morse 
code. Lord Kelvin's Siphon Recorder is an instrument 
which writes the signals upon a strip of paper by the 
following ingenious means: — The cable communicates 
with a delicately-suspended coil of wire that hangs be- 
tween the poles of a powerful magnet. To the suspended 
coil is attached a fine siphon of glass suspended by a silk 
fi.bre, one end of which dips into an ink vessel. The ink 
makes marks upon a strip of paper (moved by clockwork 
vertically past the siphon), friction being obviated by 
giving the siphon a continual minute vibration. The 
siphon record is a wavy line having short and long waves 
for dots and dashes. 



Lesson LII. — Miscellaneous Telegraphs 

507. Multiplex Telegraphs. — Varley proposed to 
send messages by transmitting electrically musical tones, 
interrupted to sound as dots and dashes. This necessi- 
tated the transmission of currents either rapidly alternat- 



544 ELECTRICITY AND MAGNETISM part ii 

iiig or rapidly intermittent. Gray, who constructed 
harmonic telegraphs on this plan, found it possible to 
transmit five or six messages simultaneously in one line. 

By using at each end of a line two synchronously 
revolving distributing switches, it is possible to send 
several messages at once through a line ; the distributors 
(invented by Delany) causing each transmitting instru- 
ment to be in circuit with its corresponding receiving 
instrument for a small fraction of a second at regular 
short intervals. 

508. Electric Bells. — The common form of Electric 
Trembling Bell (invented 1850 by John Mirand) consists 
of an electromagnet, which moves a hammer backward 
and forward by alternately attracting and releasing it, so 
that it beats against a bell. The arrangements of the 
instrument are shown in Fig. 285, in which E is the 
electromagnet and H the hammer. A battery, consisting 
of one or two Leclanche cells placed at some convenient 
point of the circuit, provides a current when required. 
By touching the " push " P, the circuit is completed, and 
a current flows along the line and round the coils of the 
electromagnet, which forthwith attracts a small piece of 
soft iron attached to the lever, which terminates in the 
hammer H. The lever is itself included in the circuit, 
the current entering it above and quitting it at C by a 
contact-breaker, consisting of a spring tipped with plat- 
inum resting against the platinum tip of a screw, from 
which a return wire passes back to the zinc pole of the 
battery. As soon as the lever is attracted forward the 
circuit is broken at C by the spring moving away from 
contact with the screw ; hence the current stops, and the 
electromagnet ceases to attract the armature, but the 
momentum of the hammer carries it forward. Imme- 
diately afterwards, how^ever, the hammer falls back, again 
establishing contact at C, whereupon the armature is once 
more attracted forward, and so on. The push P is shown 
in section in Fig. 286. It usually consists of a cylindri- 



CHAP. XII 



ELECTRIC CLOCKS 



545 



cal knob of ivory or porcelain capable of moving loosely- 
through a hole in a circular support of porcelain or wood, 
and which, when pressed, forces a platinum-tipped spring 




against a metal pin, and so makes electrical contact be- 
tween the two parts of the interrupted circuit. Bells, 
having a polarized armature, and without any break, 
are used as call-bells or telephones ; the generator being 
a small magneto alternator like Fig. 259, driven by a 
handle. 

509. Electric Clocks and Chronographs. — Clocks may 
be either driven or controlled by electric currents. Bain, 
Hipp, and others have devised electric clocks of the first 
kind, in which the ordinary motive-power of a weight or 
spring is abandoned, the clock being driven by its pen- 
dulum, the "bob" of which is an electromagnet alter- 
nately attracted from side to side. The difficulty of 
maintaining a perfectly constant battery current has 
prevented such clocks from coming into use. 
2n 



546 ELECTRICITY AND IklAGNETISM pakt ii 

Electrically controlled clocks, governed by a standard 
central clock, have proved a more fruitful invention. In 
these the standard timekeeper is constructed so as to 
complete a circuit periodically, once every minnte or half 
minute. The transmitted currents set in movement the 
hands of a system of dials placed at distant points, by 
causing an electromagnet placed behind each dial to 
attract an armature, which, acting upon a ratchet wheel 
by a pawl, causes it to move forward through one tooth 
at each specified interval, and so carries the hands round 
at the same rate as those of the standard clock. 

Electric chronographs are used for measuring very 
small intervals of time. A stylus fixed to the armature 
of an electromagnet traces a line upon a piece of paper 
fixed to a cylinder revolving by clockwork. A cm'rent 
sent through the coils of the electromagnet moves the 
armature and causes a lateral notch in the line so traced. 
Two currents are marked by two notches ; and from the 
interval of space between the two notches the interval of 
time which elapsed between the two currents may be cal- 
culated to the ten -thousandth part of a second if the 
speed of rotation is accurately known. The velocity with 
which a cannon ball moves along the bore of the cannon 
can be measured thus. 



CHAPTER Xin 

TELEPHONY 

Lesson LIII. — Electric Telephones 

510. Early Telephones. — The first successful attempt 
to transmit sounds electrically was made in 1861 by Reis, 
who succeeded in conveying musical and other tones by 
an imperfect telephone. In this instrument the voice 
was caused to act upon a point of loose contact in an 
electric circuit, and by bringing those parts into greater 
or less intimacy of contact (Art. 400), thereby varied the 
resistance offered to the circuit. The transmitting part 
of Reis's telephone consisted of a battery and a contact- 
breaker, the latter being formed of a tympanum or dia- 
phragm of stretched membrane, capable of taking up 
sonorous vibrations, and having attached to it a thin 
elastic strip of platinum, which, as it vibrated, beat to 
and fro against the tip of a platinum wire, so making and 
breaking contact wholly or partially at each vibration in 
exactly the same manner as is done with the carbon 
contacts in the modern transmitters of Blake, Berliner, 
etc. The receiving part of the instrument consisted of an 
iron wire fixed upon a sounding-board and surrounded 
by a coil of insulated wire forming part of the circuit. 
The rapid magnetization and demagnetization of such an 
iron core will produce audible sounds (Art. 124). If the 
current vary, the iron wire is partially magnetized or 
547 



548 ELECTRICITY AND MAGNETISM part ii 

demagnetized, giving rise to corresponding vibrations of 
varying amplitudes and forms; hence such a wire will 
serve perfectly as a receiver to reproduce speech if a good 
transmitter is used. Reis himself transmitted speech 
with his instrument, but only imperfectly, for all tones of 
speech cannot be transmitted by abrupt interruptions of 
the current, to which Reis's transmitter is prone when 
spoken into, owing to the extreme lightness of the contact : 
they require gentle undulations, sometimes simple, some- 
times complex, according to the nature of the sound. 
The vowel sounds are produced by periodic and complex 
movements in the air ; the consonants being for the most 
part non-periodic. Reis also devised a second receiver, in 
which an electromagnet attracted an elastically-supported 
armature of iron, which vibrated under the attraction of 
the more or less interrupted current. 

In 1876 Elisha Gray devised a transmitter in which 
a variable water-resistance (made by a platinum wire 
dipping into water) was acted upon by the voice. He 
designed an electromagnetic receiver. 

Telephone receivers were invented by Varley and 
Dolbear, in which the attraction between the oppositely- 
electrified armatures of a condenser is utilized in the pro- 
duction of sounds. Dolbear's receiver consists merely of 
two thin metal disks, separated by a very thin air-space. 
As the varying currents flow into and out of this con- 
denser the two disks attract one another more or less 
strongly, and thereby vibrations are set up which corre- 
spond to the vibrations of the original sound. 

In 1876 Graham Bell invented the magneto-telephone. 
In this instrument the speaker talks to an elastic 
plate of thin sheet iron, which vibrates and transmits 
its every movement electrically to a similar plate in 
a similar telephone at a distant station, causing it to 
vibrate in an identical manner, and thereby to emit 
identical sounds. The transmission of the vibrations 
depends upon the principles of magneto-electric indue- 



CHAP. XIII 



EARLY TELEPHONES 



649 




Fig. 287. 



tion explained in Lesson YIII. Fig. 287 shows Bell's 
Telephone in section. The disk D is 
placed behind a conical mouthpiece, to 
which the speaker places his mouth or 
the hearer his ear. Behind the disk is a 
magnet A A running the length of the 
instrument ; and upon its front pole, 
which nearly touches the disk, is fixed a 
small bobbin, on which, is wound a coil C 
of fine insulated wire, the ends of the 
coil being connected with the terminal 
screws FF. One such instrument is used 
to transmit, and one to receive the sounds, 
the two being connected in simple circuit. 
Xo battery is needed, for the transmitting 
instrument itself generates the induced currents as fol- 
lows : The magnet AA induces a certain number of 
magnetic lines thi'ough the coil C. Many of these pass 
into the iron disk. When the iron disk in vibrating 
moves toward the magnet-pole more magnetic lines meet 
it ; when it recedes, fewer lines meet it. Its motion to 
and fro will therefore alter the number of lines which pass 
through the hollow of the coil C, and will therefore (Art. 107) 
generate in the wire of the coils currents whose strength 
is proportional to the rate of change in the number of 
the lines. Bell's instrument, when used as a transmitter, 
may therefore be regarded as a sort of vibrating dynamo, 
which pumps currents in alternate directions into the 
wire. At the distant end the currents as they arrive 
flow round the coils either in one direction or the other, 
and therefore either add momentarily to or take from the 
strength of the magnet. When the current in the coils 
is in such a direction as to reinforce the magnet, the 
magnet attracts the iron disk in front of it more strongly 
than before. K the current is in the opposite direction 
the disk is less attracted and flies back. Hence, whatever 
movement is imparted to the disk of the transmitting 



550 ELECTRICITY AND MAGNETISM part ii 

telephone, the disk of the distant receivmg telephone is 
forced to repeat, and it therefore throws the air into 
similar vibrations, and so reproduces the sound. Bell's 
method of transmitting was soon abandoned (except for 
very short lines). In modern telephonic work Reis's 
plan of using a separate transmitter with a battery is 
universal, the Bell instrument being used as a receiver 
only and not as a transmitter. 

511. Edison's Transmitter. — Edison constructed a 
transmitting instrument, in which the vibrations of the 
voice, actuating a diaphragm of mica, made it exert more 
or less compression on a button of prepared lamp-black 
placed in the circuit. The resistance of this is affected 
by pressure of contacts ; hence the varying pressures due 
to the vibrations cause the button to offer a varying 
resistance to any current flowing (from a battery) in the 
circuit, and vary its strength accordingly. This varying 
current may be received as before in an electromagnetic 
receiver of the type described above, and there set up 
corresponding vibrations. This instrument also has been 
abandoned in favour of transmitters of the microphone 
type. Edison also invented a receiver of singular power, 
which depends upon a curious fact discovered by himself, 
namely, that if a platinum point presses against a rotating 
cylinder of moist chalk, the friction is reduced when a 
current passes between the two. And if the point be 
attached to an elastic disk, the latter is thrown into 
vibrations corresponding to the fluctuating currents 
coming from the speaker's transmitting instrument. 

512. Microphones. — Hughes, in 1878, discovered 
that a loose contact between two conductors, forming part 
of a cii'cuit in which a small battery and a receiving 
telephone are included, may serve to transmit sounds 
without the intervention of any specific tympanum or 
diaphragm like those of Reis and Edison, because the 
smallest vibrations wdll affect the resistance (Art. 400) at 
the point of loose contact. The Microphone (Fig. 288) 



CHAP. XIII 



MICROPHONES 



551 



embodies this principle. In the form shown in the 
figure, a smaU. thin pencil of carbon is supported loosely 
between two little blocks of the same substance fixed to a 
sounding-board of thin pine-wood, the blocks being con- 
nected with one or tw^o small cells arid a Bell receiver. 
The amplitude of the vibrations emitted by the receiver 
m.ay be much greater than those of the original sounds, 




Fig. 288. 



and therefore the microphone may serve, as its name 
indicates, to magnify minute somids, such as the ticking 
of a watch or the footfalls of an insect, and render them 
audible. In modern telephony microphones under the 
name of carbon transmitters are in general use. In the 
Blake transmitter a pin of platinum is pressed by a light 
spring against a polished plug of hard carbon, forming a 
delicate contact through which the current flows. This 
electrical mechanism is mounted behind a metal disk to 
take up the vibrations of the speaker's voice. In the 
Hunnings loud-speaking transmitter granulated coke 
carbon is placed loosely between two metal surfaces, so 



552 



ELECTEICITY AND MAGNETISM part ii 



that tlie current flows through the loose particles. The 
voice acts on all the loose contacts at once. 

513. Telephone Exchanges. — For enabling a large 
number of subscribers to communicate by telephone 
■^'ith one another, the lines from each subscriber's instru- 
ment are brought to a central office known as a te.leplione 
excliange. Here each line terminates on a switch-hoard 
which is so arranged that the operator can in an instant 
make a connexion from the line of any one subscriber to 
that of any other, so that these two cri talk together, 

514. Hughes's Induction Balance. — The extreme 
sensitiveness of Bell's receiver (Art. 510) to the feeblest 
currents has suggested its employment to detect currents 
too weak to affect the most delicate galvanometer. The 
currents must, however, be intermittent, or they will not 
keep the disk of the telephone in vibration. Hughes 
applied this property of the telephone to an instrument 




ilf-^l;^^^.^ 



Fig. 259. 



named the Induction Balance (Fig. 289) . A small bat- 
tery B, connected with a microphone M, passes through 
two coils of wire P^, Pg, wound on bobbins fixed on a 
suitable stand. Above each of these primary coils are 
placed two secondary coils, S^, S,, of wire, of the same 
size, and of exactly equal numbers of turns of wire. The 
secondary coils are joined to a receiver T, and are wound 
in opposite directions. The result of this arrangement is 



CHAP. XIII INDUCTION BALANCE 553 

that whenever a current either begins or stops flowing in 
the primary coils, ¥^ induces a current in S^, and Pg in 
83. As Sj and 83 are wound in opposite ways, the two 
currents thus induced in the secondary wire neutralize 
one another, and, if they are of equal strength, balance 
one another so exactly that no sound is heard in the tele- 
phone. But a perfect balance cannot be obtained unless 
the resistances and the coefficients of mutual induction 
and of seK-induction are alike. If a flat piece of silver or 
copper (such as a coin) be introduced between 8^ and Pj, 
there will be less induction in 8^ than in 83, for part of 
the inductive action in P^ is now spent on setting up 
currents in the mass of the metal (Art. 459), and a sound 
will again be heard in the telephone. But balance can 
be restored by moving 83 farther away from Pg, until the 
induction in 83 is reduced to equality with 8^, when the 
sounds in the telephone again cease. It is possible by 
this means to test the relative conductivity of different 
metals which are introduced into the coils. It is even 
possible to detect a counterfeit coin by the indication 
thus afforded of its conductivity. The induction balance 
has also been applied in surgery by Graham Bel] to 
detect the presence of a bullet in a wound, for a lump of 
metal may disturb the induction when some inches 
distant from the coils. 



CHAPTER XIY 

ELECTRIC WAVES 

Lesson LIT. — Oscillations and Waves 

615. Electric Oscillations. — If a charged condenser 
or Leyden jar is discharged slowly through a conductor 
of high resistance, such as a nearly dry linen thread, 
the charge simply dies away by a discharge which 
increases in strength at first, and then gTadually dies 
away. If, however, the condenser is discharged through 
a coil of wire of one or more turns (the S23ark be'ing taken 
between polished knobs to prevent premature partial dis- 
charges by winds or brashes) the effect is wholly different, 
for then the discharge consists of a number of excessively 
rapid oscillations or surgings. This is in consequence of 
the self-induction of the circuit, by reason of which (Art. 
458) the current once set up tends to go on. The fii-st 

rush more than empties the 
condenser, and charges it the 
opposite way ; then follows a 
reverse discharge, which also 
overdoes the discharge, and 
charges the condenser the 
same way as at first, and so 
forth. Each successive oscil- 
lation is feebler than the preceding, so that after a number 
of oscillations the discharge dies away as in Fig. 290. The 
554 




Fig. 290. 



CHAP. XIV ELECTKIC OSCILLATIONS 555 

spark of a jar so discharged really consists of a number 
of successive sparks in reverse directions. One proof of 
this, as pointed out by Henry in 1842 from the experi- 
m.ents of Savery, is that if jar discharges through a coil 
are used to magnetize steel needles, the direction of the 
magnetization is anomalous, being sometimes one way, 
sometimes the other. 

That a discharge ought under certain conditions to 
become oscillatory was noted by Von Helmholtz. Lord 
Kelvin in 1855 predicted these conditions. If the capacity 
of the condenser is K (farads), the resistance of the cir- 
cuit R (ohms), and its inductance L (henries), there will 
be oscillations if 

R<V4L/K; 

and there will be no oscillations if 
E,>V4L/K. 

In the former case the frequency n of the oscillations will 
b)e such that 

>/KL 4L ' 

Example. — U K = 0-01 microfarad, L = 000001 henry, and 
R = 0, n = 503,000. 

If E. is small n is nearly equal to 1 -f- 27rVKL. 

The oscillations can be made slower by increasing either 
K or L. The oscillations of an ordinary Leyden jar dis- 
charge may last only from a ten-thousandth to a ten- 
millionth of a second. By using coils of well-insulated 
wire and large condensers, Lodge has succeeded in slowing 
down the oscillations to 400 a second ; the spark then 
emitting a musical note. Iron is found to retain its 
magnetic properties even for oscillations of the frequency 
of one million per second. 

Feddersen subsequently examined the spark of a 
Leyden jar by means of a rotating mirror, and found that 



556 ELECTRICITY AND MAGNETISM part ii 

instead of being a single instantaneous discharge, it 
exhibited definite fluctuations.* With very small resist- 
ances in the circuit, there was a true oscillation of the 
electricity backward and forward for a brief time. The 
period of the oscillations was found to be proportional to 
the square root of the capacity of the condenser. With 
a certain higher resistance the discharge became continu- 
ous but not instantaneous. With a still higher resistance 
the discharge consisted of a series of partial intermittent 
discharges, following one another in the same direction. 
Such sparks when viewed in the rotating muTor showed 
a series of separate images at nearly equal distances apart. 

516. Electric Waves. — Though the increasing and 
dying away of currents, for example in cables, is some- 
times loosely described as of " waves " of current, these 
phenomena are very different from those of true electric 
or electromagnetic ivaves propagated across space. In the 
case of true electric waves, portions of the energy of the 
current or discharge are thrown off from the conductor 
and do not return back to it, but go travelling on ui 
space. If a current increases in strength the magnetic 
field around it also increases, the magnetic lines enlarging 
from the conductor outward, like the ripples on a pond. 
But as the current is decreased the magnetic Imes all 
return back and close up upon the conductor ; the energy 
of the magnetic field retmms back into the system. But 
if for CTU'rents slowly waxing and waning.we substitute 
electric oscillations of excessive rapidity, part of their 
energy radiates off into the surrounding medium as 
electromagnetic ivaves, and only part retm^ns back. As 
will be presently set forth, these waves possess all the 
optical properties of light-waves, and can be reflected^ 
refracted, polarized, etc. 

It is a fundamental part of the modern views of electric 
action that while an electric displacement (Art. 57) is 

* These electric oscillations were examined also by Schiller, Over' 
beck, Blaserna, and others, notably by Hertz ; see Art. 520 below. 



CHAP. XIV 



EESONANCE 



557 



being produced in a dielectric, the effect in surrounding 
space is the same as if there had been a conductive instead 
of an inductive transfer of electricity. Maxwell gave the 
name of displacement-current to the rate of change of 
the displacement. Experiment proves that displace- 
ment-currents, while they last, set up magnetic fields 
around them ; just as convexion-currents (Art. 397) and 
conduction-currents do. 

517. Resonance. — The circumstance that when 
certain definite relations exist between the capacity and 
inductance of a circuit and the frequency of the periodic 
cm-rents, the choking reactions of these properties neu- 
tralize one another, has been ah'eady alluded to in Art. 
473. And we have seen (Art. 515) that a circuit with a 
certain self-induction, capacity, and resistance tends to 
oscillate electrically at a certain frequency. If it be 
placed in a medium through which electric waves of that 
frequency are passing in such a position that the electric 
and electromagnetic fields of the successive waves can 
induce cm^rents in it, each wave will give a slight im- 
pulse to the readily-excited oscillations, which will grow 
in intensity, just as small impulses given to a pendulum 
at the right times w^ill make it swing violently. 

The following experiment of Oliver Lodge beautifully 
illustrates this phenomena of resonance, and at the same 
time the production of waves 



by an oscillatory discharge. 
Two Leyden jars, Fig. 291, 
are placed a little way apart 
from one another. One of 
them, charged from an in- 
fluence machine not shown, 
is provided with a bent wire 
to serve as a discharging 
circuit, with a spark-gap S 




Fig. 291. 



between the polished knobs at the top. The second jar is 
provided with a circuit of wire, the inductance of which 



558 ELECTRICITY AND MAGNETISM part ii 

can be adjusted by sliding in or out a cross-piece W 
hooked upon the other portions. A strip of tinfoil is 
brought up from the inner coating over the lip of this 
jar, but does not quite touch the outer coating. If the 
two cii'cuits are properly tuned together, whenever a 
spark passes in the gap at the top of A, surgings will 
be set up in the circuit of B which will cause the jar to 
overflow, producing a spark at the end of the strip. 



Lesso:n" LV. — The Electromagnetic Theory of Light 

518. Maxwell's Theory.— In 1867 Clerk Maxwell 
put forward the theory that the waves of light are not 
mere mechanical motions of the ether, but that they are 
electrical undulations. These undulations are partly 
electrical and partly magnetic, oscillating electrical dis- 
placements being accompanied by oscillating magnetic 
fields at right angles to them, whilst the direction of 
propagation of the wave is at right angles to both. 
According to this theory the phenomena of electro- 
magnetism and the phenomena of light are all due to 
certain modes of motion in the ether, electric currents 
and magnets being due to streams and whirls or other 
bodily movements in the substance of the ether, while 
light is due to vibrations to and fro in it. 

An electric displacement in its growth or decay pro- 
duces a magnetic force at right angles to itself; it also 
produces (by the peculiar action known as induction, 
an electric force which is propagated at right angles 
both to the electric displacement and to the magnetic 
force. Now it is known that in the propagation of 
light the actual displacements or vibrations which con- 
stitute the so-called ray of light are executed in du-ections 
at right angles to the direction of propagation. This 
analogy is an important point in the theory, and imme- 
diately suggests the question whether the respective rates 



CHAP. XIV 



MAXWELL'S THEORY 



559 



of propagation are the same. Xow the velocity of propa- 
gation of electromagnetic induction is that velocity " v " 
which was shown (Art. 359) to represent the ratio between 
the electrostatic and the electromagnetic units, and which 
(in air) has been found to be 

2-9857 X lOi*^ centimetres per second. 

And the velocity of light (in air) has been repeatedly 
measured (by Fizeau, Cornu, Michelson, and others), 
giving as the approximate value 

2-9992 X 10^° centimetres per second. 

From the equations for the propagation of a disturb- 
ance in an electromagnetic medium, having dielectric 
coefficient k (Art. 295) and permeability fx (Art. 363), it 
was calculated by Maxwell that the velocity ought to be 
numerically = 1/ y/k/x. And, as we have seen, this quan- 
tity enters into the ratio of the units (Art. 360), and 
can be calculated from them. It follows that if there 
are two transparent media of equal permeability, but 
different dielectric capacities, the velocities in them ought 
to vary relatively inversely as Vk. But the ratio of the 
velocities of light in them is called their refractive index. 
Hence if Maxwell's theory is true, the dielectric capacity 
of ordinary transparent media ought to be equal to the 
square of the refractive index. Experiments by Gordon, 





k. 


(Index)2. 


Flint Glass 
Bisulphide of Carbon 
Sulphur (mean) 
Paraffin 


3-162 
1-812 
4-151 
2-32 


2-796 
2-606 
4-024 
2-33 



Boltzmann, and others, show this to be approximately 
true for waves of very great wave-length. The values 



560 ELECTRICITY AND MAGNETISM part ii 

are shown below. For gases the agreement is even 
closer. 

Another consequence of the theory is that all con- 
ductors, since they dissipate the energy of the currents set 
up in them, ought to be opaque to light. Metallic con- 
ductors are, except when in very thin films. But electro- 
lytic liquids are not opaque, the mechanism of their con- 
duction being different (Art. 490). In some crystalline 
bodies which conduct electricity better in one direction 
than in another, the opacity to light differs correspond- 
ingly. Coloured crystals of Tourmali7ie conduct electricity 
better across the long axis of the crystal than along that 
axis. Such crystals are much more opaque to light pass- 
ing along the axis than to light passing across it. And, 
in the case of rays traversing the crystal across the axis, 
the vibrations across the axis are more completely ab- 
sorbed than those parallel to the axis : whence it follows 
that the transmitted light will be polarized. 

519. Energy Paths. — From Maxwell's equations 
Poynting in 1883 drew the conclusion that in all cases 
where energy is transferred in an electric system it flows 
parallel to the surfaces of both electric and magnetic 
equipotentials. What we call an electric current along 
a wire is rather a transfer of energy by an invisible 
mechanism in the medium outside the wire. Wherever 
in the wire there is resistance, wasting energy by degrad- 
ing it into heat, at that point energy flows in laterally from 
the medium. According to this view, the service of the 
wire is merely to guide the energy flow going on outside 
it.* We know that when a current is started much 
energy is spent in building up around the conductor a 
magnetic field, the amount spent being ^^LC^ (Art. 458). 
When the circuit is "broken" this energy flows on lat- 
erally into the whe, giving rise to the so-called extra- 
current sparks. According to Poynting's view, which 
has been independently elaborated by Heaviside, all the 

* See particularly Oliver Lodge's Modern Views of Electricity. 



CHAP. XIV 



RESEARCHES OF HERTZ 



561 



energy flows in similarly. In the case of the transfer of 
energy in an alternate current transformer from the coils 
of the primary circuit to those of the secondary, it is pretty 
obvious that the flow of energy must take place laterally 
to the copper wu-es ; and it also takes place laterally to 
the iron wires of the core, though this is not so obvious. 

520. Researches of Hertz. — In 1888 Hertz found 
the most convincing experimental proofs of Maxwell's 
theory, and succeeded in producing electromagnetic waves 
in a way which permitted him to examine their propaga- 
tion through space, and to show that, while they were 
much larger than ordinary waves of light, they possessed 
the same properties, travelled at the same speed, and were 
capable of being reflected, refracted, polarized, etc. 

Of the power of oscillatory discharges to propagate 
disturbances in the surrounding space something was 




OSCILLATOR. 

Fiff. 292. 



RESONATOR. 

Fig-. 298. 



already known. Henry had shown that they set up 
other sparks in distant conducting circuits. It had been 
discovered* that a spark-gap in the exciting circuit was 
necessary. Fitzgerald had definitely proposed to start 
waves by the oscillatory discharges of small condensers. 
But no one had systematically followed out the phe- 
nomena of propagation of the waves. 

Hertz employed to start the waves an apparatus called 
an oscillator (Fig. 292), consisting of two metallic con- 
ductors (baUs or plates) united by a metal rod, at the 

* See paper by tlie author in the Philosophical Magazine (Septem- 
ber, 1ST6). 

2o 



562 



ELECTRICITY AND MAGNETISM pakt ii 



middle of which was interposed a spark-gap between two 
well-polished knobs. And to detect the waves at a 
distance he employed a resonator, simply a cu'cle or square 
of wire, having in it a spark-gap capable of minute 
adjustment. In one experiment the oscillator consisted 
of two zinc j)lates A and B (Fig. 292) with sides 40 cm. 
long mounted 60 cm. apart, and having stout copper 
wires leading to a spark-gap between very brightly 
polished brass balls. A dry wood stand was a sufficient 
insulator. The resonator to match was a circle 35 cm. 
in radius. To experiment with this apparatus the 
oscillator is joined to a small induction coil. When 




Fig. 294. 

a spark snaps across the gap it sets up a temporary con- 
ducting path for the surgings that follow. For a rush of 
current from left to right overcharges the right-hand plate, 
and so there follows a rush back from right to left, and so 
on. Each spark sent by the coil across the gap consists of a 
dozen or so oscillations each lasting less than 1/100,000,000 
of a second, the period being determined (Art. 515) by the 
capacity and inductance of the apparatus; the discharges 
surging backward and forward from A to B until they 
die out (Fig. 290). Let the line drawn horizontally in 
Fig. 294 be termed the base line, and let the line AB be 
termed the line of oscillation. Then if the resonator is 
placed with its centre on the base line at a few feet away 
from the oscillator and is turned into various positions, 



CHAP. xiT RESEAKCHES OF HERTZ 



503 



various effects are observed. If the resonator is set 
edge-on vertically, no sparks are observed in it whatever 
the situation of the gap in the circle. If it is laid edge- 
on horizontaUj sparks pass between the balls of the 
resonator. These are brightest when the gap-space is 
nearest toward the oscillator, so that the induced spark 
is parallel to the primary spark. If the resonator be 
now turned broadside on to the oscillator it will be found 
that there are sparks when the gap is at the top or 
bottom of the circle -so that the sparks are parallel to 
the primary spark; but there are none if the gap is at 
the side. The primary spark does not here induce sparks 
at right angles to itself. 

The reflexion of electric waves was observed in various 
ways, n right opposite the oscillator. Fig. 292, is set a 
large metal sheet as a reflector, to send back the waves 
that pass along the base line, stationary nodes will be 
produced at regular intervals. H the resonator is put 
broadside on, with its gap at the highest point, and 
moved along the base line till it lies flat against the 
reflector, there will in this position be no sparks; but if 
it IS slowly moved back from the sheet sparks will show, 
will come to a maximum, then die out as the first node 
is reached at about 180 cm. from the reflector. Passing 
this node the sparks will begin again, nodes occurring at 
equal intervals apart along the base line. By using 
large parabolic mirrors Hertz showed that these electric 
waves can be reflected and brought to a focus exactly as 
light waves can be. Hertz also showed refraction with a 
prism of pitch ; and polarization by means of gratings of 
parallel wires. 

Later Tesla showed that the Hertzian effects could be 
much augmented by increasing the suddenness of the 
^ark by using a magnetic field to blow it out. Elihu 
Ihomson uses an air-blast across the spark-gap for the 
same purpose. 

521. Detectors of Electric Waves. — The Hertz spark- 



564 ELECTRICITY AXD MAGNETISM part ii 

gap resonator is only one means of detecting electric 
waves. A prepared frog's leg (Art. 255) may be nsed 
instead of a spark-gap. A sensitive vacuum tube, espe- 
cially if primed by application with a battery of some 
hundreds of small cells not quite able of themselves to 
start a spark, forms a good explorer. Electrometers; 
thin wires capable of expanding when heated by the 
induced currents ; and galvanometers in circuit with the 
gap, are amongst the possible means. Best of all is Lodge's 
device of a tube partly filled with coarse iron filings, in- 
serted in circuit with a galvanometer and a single cell. 
The resistance of the filings is very great, and little 
current flows, until an electric wave impioges upon the 
tube, when at once the filings conduct (compare Art. 400 
on conductance of powders). On lightly tapping the 
tube the filings fall back into their former state. Using 
such a detector, and an oscillator consisting of a highly 
polished brass ball between two smaller balls. Lodge has 
shown how these electric waves can pass hundreds of feet 
through walls and floors of houses. Care must be taken to 
screen off with metallic screens the effects of stray sparks. 
522. Properties of Electric Waves. — The universal 
equation connecting frequency ?i, wave-length \, and 
velocity of propagation v is : v = nX. Taking v (in 
air) as 3 x 10^° (cms. per sec.) as the velocity of light, 
and the measured length of the red waves (the longest 
visible) as 0-000076, it foUows that the frequency of 
oscillation of these must be no less than 395 x 10^^, 
The waves artificially produced by electric oscillations 
are of much lower frequency than these, and their wave- 
length proportionally longer. Their wave-length depends 
on the size of the apparatus used as oscillator, just as 
the note emitted by an iron cylmder when struck on 
its end depends on the length of the cylinder. The wave- 
length of waves emitted from an oscillator consisting 
of a wire with a small capacity at each end is twice 
the length of the wire. That of waves emitted from 



CHAP. XIV PROPEKTIES OF ELECTRIC WAVES 565 




Fig. 295. 



a sphere (Fig. 295) of diameter d is 27r<^/V3 or 3-6 d: 
but they die out after about 1 vibration. If a spark-gap 
is made between two knobs across the diameter of a 
hollow cylinder, the wave- 
length of the waves emitted 
from the end of the cylinder 
is about equal to its diameter, 
and the vibrations are numer- 
ous before all the energy has 
been radiated away. Using 

symmetrical pairs of conden- , _^ 

sers carefully adjusted Ebert J/ 
has obtained oscillations that "^ 
do not die out till after 20,000 
periods. 

The currents produced in 
wires by oscillations of such enormous frequency are only 
skin-currents (Art. 476), the inner part of the wire being 
idle. Hence for such currents the impeding resistance 
of a stout copper wire may be 
millions of ohms. One evidence 
of this is afforded by the tendency 
to lateral discharge. This is 
readily shown by connecting 
between the Ley den jars of an 
influence machine a loop of stout 
copper wire bent as in Fig. 296. 
When a discharge takes place 
between the knobs, there will be 
an oscillatory current set up 
between the outer coatings also ; and this oscillatory 
current rather than flow along the metal loop will jump 
as a spark across the parts that lie nearest together. The 
tendency of lightning to produce lateral discharges is 
relied upon by Oliver Lodge in his contention as to the 
oscillatory character of the flash. 

523. Travelling of Waves along Wires. — If an 




Fig. 296. 



566 



ELECTRICITY AND MAGNETISM part ii 



G 



oscillatory spark is sent into one end of a long wire, by 
the time that the second pulsation reaches its maximum 
the first will have travelled a certain distance which may 
be called the wave-length of the disturbance. According 
to Maxwell's theory the velocity of propagation will be 
equal to that of light, the energy really travelling through 
the air, and settling down laterally into the 
ware. It appears from experiment that the 
velocity of a wave guided by a wire is 
the same as that of a wave travelling in 
free air. That the speed of travelling is 
independent of the thickness or materials of 
the wire was proved in 1870 by Yon Bezold 
using the device of Fig. 297. Let an 
oscillatory discharge be sent by a wke at G 
into a rectangular circuit ABCD, having a 
spark-gap PQ midway between B and D. 
It is evident that if G is midway between 
A and C the impulses W'ill arrive simultaneously at P 
and Q, if both sides of the system are alike ; and there 
will be no spark. If now one side, say CD, be made of 
iron and the other, AB, of copper, it will be foimd that 
still the discharge must be led m at G, exactly midway 



B PQ 

Fig. 29T. 



if there is to be no spark. 



Lesson LYI. — Other Relations between Light and 
Electricity 



524. Electro-optical Phenomena. — Of late years 
several important relations have been observed between 
electricity and light. These observations may be classi- 
fied under the following heads : — 

(i.) Production of double refraction by dielectric 

stress. 
(ii.) Rotation of plane of polarization of a wave of 



CHAP. XIV ELECTROSTATIC OPTICAL STRESS 667 

light on traversing a transparent medium placed 

in a magnetic field, or by reflexion at the surface 

of a magnet, 
(iii.) Change of electric resistance, exhibited by 

selenium and other bodies during exposure to 

light, 
(iv.) Photo-chemical excitation of electromotive forces, 
(v.) Relation between refractive index and dielectric 

capacity of transparent bodies, 
(vi.) Electric effect of ultra-violet light. 

It was announced by Mrs. SomervlUe, by Zantedeschi, and 
others, that steel needles could be magnetized by exposing 
portions of them to the action of violet and ultra-violet rays of 
light ; the observations were, however, erroneous. 

Bidwell has found that light falling upon a recently de- 
magnetized piece of iron produces an instantaneous revival of 
magnetism. 

525. Electrostatic Optical Stress. — In 1875 Dr. Kerr 
of Glasgow discovered that glass when subjected to a 
severe electrostatic stress undergoes an actual strain, 
which can be observed by the aid of a beam of polarized 
light. In the original experiment two wires were fixed 
into holes drilled in a slab of giass, but not quite meeting, 
so that when these were placed in connexion with the 
terminals of an induction coil or of an influence machine 
the accumulating charges on the wires subjected the 
intervening dielectric to an electrostatic tension along 
the electric lines of force. The slab when placed between 
two Mcol prisms as polarizer and analyzer* exhibited 
double refraction, as if it had been subjected to a pull 
and had expanded along the direction of the electric 
force. Bisulphide of carbon and other insulating liquids 
exhibit similar phenomena, but fatty oils of animal and 

* A ray of light is said to be polarized if the vibrations take place in 
one plane. Ordinary light can be reduced to this condition by passing it 
through a suitable polarizing apparatus (such as a Nicol prism, a thin slice 
of tourmaline crystal, etc.)- 



568 ELECTRICITY AND MAGNETISM part ii 

vegetable origin exhibit an action in the negative direc- 
tion, as if they had contracted along the electric lines. 
It is found that the difference of retardation between 
the ordinary and extraordinary waves per unit thickness 
of the dielectric is proportional to the square of the result- 
ant electric force. The axis of double refraction is 
along the line of the electric force. Quincke has pointed 
out that these phenomena can be explained by the exist- 
ence of electrostatic expansions and contractions stated 
in Art. 300. 

526. Magneto-optic Rotation of the Plane of Polari- 
zation of Light. — In 1845 Faraday discovered that a 
wave of light polarized in a certain plane can be twisted 
round by the action of a magnet, so that the vibrations 
are executed in a different plane. The plane in which a 
beam is polarized can be detected by observing it through 
a second Xicol prism (or tourmaline), for each such 
polarizer is opaque to waves polarized in a plane at right 
angles to that plane in which it would itself polarize 
light. Faraday caused a polarized beam to pass through 
a piece of a certain " heavy glass " (consisting chiefly of 
borate of lead), lying in a powerful magnetic field, be- 
tween the poles of a large electromagnet, through the 
coils of which a current could be sent. In the path of 
the emerging beam was placed as analyzer a second Xicol 
prism which had been turned round until all the light 
was extinguished. In this position its own plane of sym- 
metry was at right angles to the plane of polarization of 
the beam. On completing the circuit, light was at once 
seen through the analyzing Nicol prism, proving that the 
waves had been twisted round into a new position, in 
which the plane of polarization was no longer at right 
angles to the plane of symmetry of the analyzer. But if 
the analyzing Nicol prism was itself turned round, a new 
position could be found (at right angles to the plane of 
polarization of the waves) at which the light was once 
more extinguished. The direction of the magneto-optic rota- 



CHAP. xiT ROTATION OP LIGHT- WAVES 569 

tion of the plane of polarization is the same (for diamagnetic 
media) as that in which the current flows which produces the 
magnetism. Yerdet discovered the important law that, 
with a given material, the amount of rotation is propor- 
tional to the strength of the magnetic force H. In case the 
waves do not pass straight along the direction of the 
field, the amount of rotation is proportional to the cosi^ie 
of the angle j3 between the direction of the beam and the lines 
of force. It is also proportional to the length I of the 
material through which the waves pass. These laws are 
combined in the equation for the rotation 6 : 

0=w'B.'cos^-l, 

where iv is a coeflBcient which represents the specific 
magnetic rotatory power of the given substance, and is 
known as Verdefs constant. ^STow, H • cos /3 • Z is the 
difference of magnetic potential between the point A 
where the wave enters and B where it leaves the medium. 
Hence 

w= ^ . 
Vb - Va 

The value of Yerdet's constant for yellow sodium 
light, at 18° C, has been carefully determined. Its value 
(in radians per unit fall of magnetic potential) is, in 
bisulphide of carbon 1-222 x 10"^; in water 0-375 x 10-^; 
in heavy glass 2-132 x 10"^. For diamagnetic substances 
the coefiicient is usually positive ; but in the case of 
many magnetic substances, such as solutions of ferric 
chloride, has a negative value (i.e. in these substances the 
rotation is in the opposite direction to that in which the 
magnetizing current flows). The phenomenon discovered 
by Hall (Art. 397) appears to be intimately related to 
the phenomenon of magneto-optic rotation. For light 
of different colours the rotation is not equal, but varies 
very nearly inversely as the square of the wave-length. 

Gases also rotate the plane of polarization of light in 



570 ELECTRICITY AND MAGNETISM part ii 

a magnetic field with varying amounts ; coal-gas and 
carbonic acid being more powerful than air or hydrogen ; 
oxygen and ozone being negative. The rotation is in all 
cases very slight, and varies for any gas in proportion to 
the quantity of gas traversed. H. Becquerel has shown 
that the plane of the natural polarization of the sky does 
not coincide with the plane of the sun, but is rotated by 
the influence of the earth's magnetism through an angle 
which, however, only reached 59' of arc at a maximum 
on the magnetic meridian. 

We have seen (Arts. 126, 397, and 398) what evidence there 
is for thinking that magnetism is a phenomenon of rotation, there 
being a rotation of something around an axis lying in the direction 
of the magnetization. Such a theory would explain the rotation 
of the plane of polarization of a ray passing through a magnetic 
field. For a ray of plane-polarized light may be conceived of as 
consisting of a pair of (oppositely) circularly-polarized waves, in 
which the right-handed rotation in one ray is periodically counter- 
acted by an equal left-handed rotation in the other ray ; and if 
such a motion were imparted to a medium in which there were 
superposed a rotation (such as we conceive to take place in every 
magnetic field) about the same direction, one of these circularly- 
polarized rays would be accelerated and the other retarded, so 
that, when they were again compounded into a single plane- 
polarized ray, this plane would not coincide with the original 
plane of polarization, but would be apparently turned round 
through an angle proportional to the superposed rotation. 

527. Kerr's Effect. — Dr. Kerr showed in 1877 that 
a ray of polarized light is also rotated when reflected 
at the surface of a magnet or electromagnet. When the 
light is reflected at a pole the plane of polarization is 
turned in a direction contrary to that in which the 
magnetizing current flows. If the light is reflected at a 
point on the side of the magnet it is found that when 
the plane of polarization is parallel to the plane of 
incidence the rotation is in the same direction as that 
of the magnetizing current; but that, when the plane of 
polarization is perpendicular to the plane of incidence, 
the rotation is in the same direction as that of the 



CHAP. XIV PROPERTIES OF SELENIUM 571 

magnetizing current only when the incidence exceeds 
75°, being in the opposite direction at lesser angles of 
incidence. 

528. Kundt's Effect. — Kundt found that the plane 
of polarization of light-waves is also rotated if the light 
is passed through a film of iron so thin as to be trans- 
parent, if placed transversely in a magnetic field. 

529. Photo-electric Properties of Selenium. — In 
1873 Willoughby Smith announced the discovery (by 
J. E. Mayhew), that the element selenium possesses the 
abnormal property of changing its electric resistance 
under the influence of light. Ordinary fused or vitreous 
selenium is a very bad conductor; its resistance being 
nearly forty-thousand-million (3 • 8 x 10^*^) times as great 
as that of copper. When carefully annealed (by keeping 
for some hours at a temperature of about 220° C, just 
below its fusing point, and subsequent slow cooling) it 
assumes a crystalline condition, in which its electric 
resistance is considerably reduced. In the latter condi- 
tion, especially, it is sensitive to light. Adams found 
that greenish-yellow rays were the most effective. He 
also showed that the change of electric resistance varies 
directly as the square root of the illumination, and that the 
resistance is less with a high electromotive-force than a 
low one. In 1879, Graham Bell and Sumner Tainter 
devised "selenium cells," in which annealed selenium 
is formed into narrow strips between the edges of broad 
conducting plates of brass, thus securing both a reduction 
of the transverse resistance and a large amount of surface- 
exposure to light. Thus a cell, whose resistance in the 
dark was 300 ohms, when exposed to sunlight had a 
resistance of but 150 ohms. This property of selenium 
these investigators applied in the construction of the Pho- 
tophone, an instrument which transmits sounds to a 
distance by means of a beam of light reflected to a 
distant spot from a thin mirror thrown into vibrations 
by the voice ; the beam falling, consequently, with 



572 ELECTRICITY AND MAGNETISM part ii 

varying intensity upon a receiver of selenium connected 
in circuit with a small battery and a Bell telephone 
receiver (Art. 510) in which the sounds are reproduced 
by the variations of the cm-rent. 

Similar properties are possessed, to a smaller degree, 
by tellurium. Carbon is also sensitive to light. 

530. Photo-chemical Cells. — About the middle of 
the present century Becquerel showed that when two 
plates of silver, coated with freshly deposited chloride of 
silver, are placed in a cell with water and connected with 
a galvanometer, a current is observed to pass when light 
falls upon one of the two plates, the exposed plate acting 
as an anode ; and Minchin has more recently shown the 
efficiency of other photo-chemical combinations. Some 
of these are very sensitive to electric waves of greater 
wave-length. 

531. Photo-electric Loss of Charge. — In 1887 Hertz 
made the discovery that a spark starts more readily 
between the baUs of a discharger when illuminated by 
light that is rich in violet and ultra-violet rays (magne- 
sium light, arc light, or spark of induction coil) than 
when not so illuminated. The effect varies with dif- 
ferent metals, with theu' cleanness, the nature of the 
sm-rounding gas, with the kind of charge, and with the 
polarization of the light. In ultra-violet light freshly 
polished zinc in air rapidly discharges a negative charge, 
but not a positive one. On the other hand the peroxides, 
in an atmosphere of hydrogen, when so illuminated 
readily discharge positive charges. The effect is stronger 
when the plane of the vibration of the incident waves is 
at right angles to the surface than when the polarization 
is in a parallel plane. The phenomenon appears to be 
due to the small light-waves stimulating chemical re- 
actions which do not occur except (Art. 322) by a species 
of electric exchange. In a strong magnetic field no such 
discharges occur. Hallwachs charged clean zinc plates 
positively by exposure to ultra-violet light. 



APPENDIX A — 



em 

Degrees. 


0in c, 
Eadians. "^ 


ine e. Tar 


gent e. 


Solid Angle 
27r(l-cos0). 


Complement 


0° 














90° 


1 


•0175 


0175 


0175 


•000957 


89 


2 


•0349 


0349 


0349 


•003S37 


88 


3 


•0524 


0523 


05-24 


•00861 


87 


4 


•0698 


0698 


0699 


•01532 


86 


5 


•0873 


0872 


0875 


•02391 


85 


6 


•1047 


1045 


1051 


•03441 


84 


7 


•1222 


1219 


1228 


•04683 


83 


8 


•1396 


1392 


1405 


•06115 


82 


9 


•1571 


1564 


1584 


•07735 


81 


10 


•1745 


1737 


1763 


•09545 


80 


11 


•1920 


1908 


1944 


•1154 


79 


12 


•2094 


2079 


2126 


•1373 


78 


13 


•2269 


2250 


2309 


•1610 


77 


14 


•2444 


2419 


2493 


•1866 


76 


15 


•2618 


2588 


26S0 


•2140 


75 


16 


•2793 


2756 


2868 


•2434 


74 


IT 


•2967 


2924 


3057 


•2745 


73 


IS 


•3142 


3090 


3249 


•3075 


72 


19 


•3316 


3256 


3443 


•3423 


71 


20 


•3491 


3420 


3640 


•3789 


70 


21 


•3665 


35S4 


3839 


•4173 


69 


22 


•3840 


3746 


4040 


•4575 


68 


23 


•4014 


3907 


4245 


•4994 


67 


24 


•4189 


4067 


4452 


•5431 


66 


25 


•4363 


4226 


4663 


•5886 


65 


26 


•4538 


4384 


4877 


•6358 


64 


27 


•4712 


4540 


5095 


■6848 


63 


28 


•4887 


4695 


5317 


•7354 


62 


29 


•5062 


4848 


5543 


•7877 


61 


30 


•5236 


5000 


5774 


•8417 


60 


31 


•5411 


5150 


6009 


•8974 


59 


32 


•5585 


5299 


6249 


•9507 


58 


33 


•5760 


5446 


6494 


1^0136 


57 


34 


■5934 


5592 


6745 


1-0741 


56 


35 


•6109 


5736 


7002 


1-1362 


55 


36 


•6283 


5878 


7265 


M999 


54 


37 


•64.53 


6018 


7536 


1^2652 


53 


38 


•6632 


6157 


7813 


1-3319 


52 


39 


•6807 


6293 


S098 


1-4002 


51 


40 


•6981 


6428 


8391 


1-4700 


50 


41 


•7156 


6561 


8693 


1-5412 


49 


42 


•7330 


6691 


9004 


1-6138 


48 


43 


•7505 


6820 


9325 


1-6879 


47 


44 


•7679 


6947 


9657 


1-7634 


46 


45 


•7854 


7071 1 


0000 


1-8402 


45 




C( 


)sine Cota 


ngent <}> 


2n(l-sin<f)) 


01n Degrees 



574 



ANGLES AND SOLID ANGLES 



Degrees. 


01n 
Eadians. 


Sinefl. 


Tangent 0. 


Solid Angle 
277(1 — cos 0). 


Complement 
of0=<^. 


4-53 


•7S54 


•7071 


1-0000 


r8402 


450 


•46 


•8029 


•7193 


1-0355 


1-9185 


44 


47 


•8203 


•7314 


1 •07-24 


1-9930 


43 


43 


•8373 


•7431 


1^1106 


2-0789 


42 


49 


•8552 


•7547 


1^1504 


2-1610 


41 


50 


•8727 


•7660 


1-1918 


2-2444 


40 


51 


•8901 


•7772 


1-2349 


2-3290 


39 


52 


•9076 


•7880 


1-2799 


2-4149 


38 


53 


•9250 


•7986 


1-3270 


2-5019 


37 


54 


•9425 


•8090 


1-37&4 


2-5900 


86 


55 


•9599 


•8192 


1-4282 


2-6793 


35 


56 


•9774 


•S290 


1-4826 


2-7696 


34 


5T 


•9943 


•8387 


1-5399 


2-8611 


33 


53 


1-0123 ■ 


•8481 


1^6003 


2-9536 


82 


59 


1-0293 


•8572 


1-6643 


3-0472 


81 


60 


1-0472 


•8660 


1-7321 


3-1416 


30 


61 


1-0647 


•8746 


1^8041 


3-2370 


29 


62 


1-0321 


•8830 


1^8807 


3-3334 


28 


63 


1-0996 


•8910 


1^9626 


3-4307 


27 


64 


1-1170 


•8983 


2-0503 


3-5288 


26 


65 


1-1345 


■9063 


2-1445 


8-6278 


25 


66 


1-1519 


•9136 


2-2460 


3-7276 


24 


67 


1-1694 


•9205 


2-3559 


3-8281 


23 


63 


1^1868 


•9272 


2-4751 


3-9295 


22 


69 


1^2043 


•9336 


2-6051 


4-0315 


21 


70 


r2217 


•9397 


2-7475 


4-1342 


20 


71 


1-2392 


•9455 


2-9042 


4-2376 


19 


72 


1-2566 


•9511 


3-0777 


4-3416 


18 


73 


1-2741 


•9563 


3-2709 


4-4462 


17 


74 


1-2916 


•9613 


3-4874 


4-5513 


16 


75 


1^3090 


•9659 


3-7321 


4-6570 


15 


76 


1-3265 


•9703 


4-0108 


4-7632 


14 


77 


1 -34:39 


' -9744 


4-3315 


4-8698 


13 


78 


1-3614 


•9782 


4-7046 


4-9768 


12 


79 


1-3733 


•9816 


5-1446 


5-0843 


11 


SO 


1-3963 


•9848 


5-6713 


5-1921 


10 


81 


1-4137 


•9377 


6-3133 


5-3003 


9 


32 


1-4;312 


•9903 


7-1154 


5-4087 


8 


83 


1-4486 


•9926 


8-1444 


5-5174 


7 


34 


1-4661 


•9945 


9-5144 


5-6264 


6 


85 


1-4335 


•9962 


11-4301 


5-7356 


5 


86 


1-5010 


•9976 


14-3007 


5-8449 


4 


87 


1-5184 


•9986 


19-0811 


5-9543 


3 


83 


1^5359 


•9994 


28-6363 


6-0639 


2 


89 


1^5534 


•9999 


57-2900 


6-1735 


1 


90 


1^5703 


1-0000 


OD 


6-2832 









Cosine <f> 


Cotangent 4> 


27r(l-sin<|)) 


4> in Degreef^ 



575 



APPENDIX B 

[Abstract of Bulletin of U. S. Coast and Geodetic 
Survey, dated Dece\[ber 27, 1893] 

UNITS OF ELECTRICAL :\IEASURE 

During the past few years the advance of knowledge and 
experience among electricians was such as to' indicate that the 
time was rii^e for the general adoption of the principal units of 
electrical measure. An International Congress of Electricians 
was aranged for, to meet in Chicago, during the TVorld's Colum- 
bian Exposition of 1893. In this Congress the business of detin- 
ing and naming units of measure was left to what was known 
as the " Chamber of Delegates," a body composed of those only 
who had been officially commissioned by their respective gov- 
ernments to act as members of said Chamber. The United 
States, Great Britain, Germany, and France were each allowed 
five delegates in the Chamber. Other nations were represented 
by three, two, and in some cases one. The principal nations of 
the world were represented by their leading electricians, and 
the Chamber embraced many of the most distinguished living 
representatives of physical science. 

The delegates representing the United States have reported 
to the Honorable the Secretary of State, under date of Novem- 
ber 6, 18i»3, giving the names and definitions of the units of 
electrical measure as unanimously recommended by the Cham- 
ber in a resolution as follows : 

'^Resolved, That the several governments represented by the 
delegates of this International Congress of Electricians be, and 
they are hereby, recommended to formally adopt as legal units 
of electrical measure tlie folloT\i.ng: As a unit of resistance, 
the international ohm, which is based upon the ohm equal to 
109 units of resistance of the Centimetre-Gramme-Second system 
of electromagnetic units, and is represented by the resistance 
offered to an unvarying electric current by a column of mercury 
at the temperature of melting ice 1J:"1521 grammes in mass, of 
a constant cross-sectional area and of the length of 10(5*3 centi- 
metres. 

576 



APPENDIX 577 



" As a unit of current, the international ampere, which is one- 
tenth of the unit of current of the C.G.S. system of electro- 
magnetic units, and which is represented sufficiently well for 
practical use by the unvarying" current which, when passed 
through a solution of nitrate of silver in water, and in accord- 
ance with accompanying specifications,* deposits silver at the 
rate of 0"001118 of a gramme per second. 

"As a imit of electromotive-force, the international volt, 
which is the electromotive-force that, steadily applied to a con- 
ductor whose resistance is one international ohm, will produce 
a current of one international ampere, and which is represented 
sufficiently well for practical use by \l%l of the electromotive- 
force between the poles or electrodes of the voltaic cell known 
as Clark's cell, at a temperature of 15° C, and prepared in the 
manner described in the accompanj'ing specification.! 

"As a unit of quantity, the international coulomb, which is 
the quantity of electricity transferred by a current of one in- 
ternational ampere in one second. 

" As a unit of capacity, the international farad, which is the 
capacity of a condenser "charged to a potential of one interna- 
tional volt by one international coulomb of electricity. 

" As a unit of work, the joule, which is equal to W units of 
work in the C.G.S. system, and which is represented sufficiently 



* In the follo^^'ing specification, the term silver voltameter means the 
arrangement of apparatus b}' means of which an electric current is passed 
through a solution of nitrate of silver in water. The silver voltameter 
measures the total electrical quantity which has passed during the time of 
the experiment, and by noting this time, the time average of the current, 
or if the current has been kept constant, the current itself can be deduced. 

In emplonng the silver voltameter to measure currents of about one 
ampere, the ibllomng arrangements should be adopted : 

The kathode on which the silver is to be deposited should take the form 
of a platinum bowl, not less than 10 centimetres in diameter and from 4 to 
5 centimetres in depth. 

The anode should be a x^late of pure silver some 30 square centimetres 
in area and 2 or 3 millimetres in thickness. 

This is supported horizontally in the liquid near the top of the solution 
by a platinum ^vire passed through holes in the plate at opposite corners. 
To prevent the disintegrated silver which is formed on the anode from 
falling on to the kathode, the anode should be wrapped round vnXh pure filter 
paper, secured at the back with sealing wax. 

The liquid should consist of a neutral solution of pure silver nitrate, 
containing about 15 parts by weight of the nitrate to 85 parts of water. 

The resistance of the voltameter changes somewhat as the current 
passes. To prevent these changes having too great an eff'ect on the cur- 
rent, some resistance besides that of the voltameter should be inserted in 
the circuit. The total metallic resistance of the circuit should not be less 
than 10 ohms. 

+ A committee, consisting of Messrs. Helmholtz, Ayrton, and Carhart, 
was appointed to prepare specifications for the Clark's cell. Their report 
has not yet been received. [It is substantially identical with the specifica- 
tion given in Appendix C, following, which is that adopted by the British 
Board of Trade.] 

2p 



578 ELECTRICITY AXD MAGNETISM 



well for practical use by the energy expended in one second by 
an international ampere in an international ohm. 

"As a unit of poorer, the loatt, which is equal to 10' units 
of power in the C.G.S. system, and which is represented suffi- 
ciently well for practical work done at the rate of one joule 
per second. 

" As the unit of induction, the henry, which is the induction 
in a circuit when the electromotive-force induced in this circuit 
is one international volt, while the inducing current varies at 
the rate of one ampere per second." 

To make the use of these units obligatory in all parts of the 
country will require an act of Congress, but in the absence of 
that, it is within the power of the Secretary of the Treasury 
to approve their adoption for use in all Departments of the Gov- 
ernment. This, indeed, is precisely the course long ago followed 
in reference to the ordinary weights and meastires of commerce 
and trade. Congress has"^never enacted a law fixing the value 
of their units, bu"t the Secretary of the Treasury was authorized 
to establish and construct standards for use"^ in the various 
Departments of the Government. Uniformity has followed on 
accotmt of the universal adoption of these standards by the 
several States. 

The Government is itself a large consumer of electricity and 
electrical machinery, and for its own protection it is important 
that units of measure be adopted. TTith the approval, there- 
fore, of the Honorable the Secretary of the Treastiry, the formal 
adoption by the Office of Standard Weights and Measures of 
the names and valties of tinits of electrical measure as given 
above, the same being in accord with the recommendations of 
the International Congress of Electricians of 1893, is hereby 
announced. 

T. C. :\IENDEXHALL, 

Superintendent U. S. Coast and Geodetic Survey, 

and of Standard Weights and Pleasures, 
Approved : 

J. G. CAELISLE, 

Secretary of the Ti^easury. 



APPENDIX C 



Official Specification fob the Pkeparation of the 
Clark Cell 

Definition of the Cell 

The cell consists of zinc or an amalgam of zinc with mer- 
cury and of mercury in a neutral saturated solution of zinc 
sulphate and mercurous sulphate in water, prepared with 
mercurous sulphate in excess. 

Preparation of the Materials 

1. The Mercury. — To secure purity it should be first treated 
with acid in the usual manner, and subsequently distilled in 
vacuo. 

2. The Zinc. — Take a portion of a rod of pure redistilled zinc, 
solder to one end a piece of copper wire, clean the whole with 
glass paper or a steel burnisher, carefully removing any loose 
pieces of the zinc. Just before making up the cell dip the zinc 
into dilute sulphuric acid, wash with distilled water, and dry 
with a clean cloth or filter paper. 

3. The Mercurous Sulphate. — Take mercurous sulphate, 
purchased as pure, mix with it a small quantity of pure mer- 
cury, and wash the whole thoroughly with cold distilled water 
by agitation in a bottle ; drain off the water, and repeat the 
process at least twice. After the last washing, drain off as 
much of the water as possible. 

4. The Zinc Sulphate Solution. — Prepare a neutral satu- 
rated solution of pure ("pure recrystallized ") zinc sulphate by 
mixing in a flask distilled water with nearly twice its weight 
of crystals of pure zinc sulphate, and adding zinc oxide in the 
proportion of about 2 per cent by weight of the zinc sulphate 
crystals to neutralize any free acid. The crystals should be 

579 



580 ELECTRICITY AXD MAGNETISM 



dissolved with the aid of gentle heat, but the temperature to 
which the solution is raised should not exceed 30^ C. Mer- 
curous sulphate treated as described in 3 should be added in 
the proportion of about 12 per cent by weight of the zinc sul- 
phate crystals to neutralize any free zmc oxide remaining, and 
the solution filtered, while still warm, into a stock bottle. Crys- 
tals should form as it cools. 

5. The Jlercurous Sulphate and Zinc Sulphate Paste. — Mix 
the washed mercurous sulphate with the zinc sulphate solu- 
tion, adding suificient crystals of zinc sulphate from the stock 
bottle to ensiu'e saturation, and a small quantity of pure mer- 
cury. Shake these up well together to form a paste of the 
consistence of cream. Heat the paste, but not above a tem- 
perature of 30^ C. Keep the paste for an hour at this temper- 
ature, agitating it from time to time, then allow it to cool; 
continue to shake it occasionally while it is cooling. Crystals 
of zinc sulphate should then be" distinctly visible, and should 
be distributed throughout the mass; if "^ this is not the case 
add more crystals from the stock bottle, and repeat the whole 
process. 

This method ensures the formation of a satiu-ated solution of 
zinc and mercurous sulphates in water. 

To set up the Cell 

The cell may conveniently be set up in a small test tube of 
about 2 centimetres diameter, and 4 or 5 centimetres deep. 
Place the mercury in the bottom of this tube, filling it to a 
depth of say O'o centimetre. Cut a cork about O'o centimetre 
thick to fit the tube ; at one side of the cork bore a hole through 
which the zinc rod can pass rightly : at the other side bore 
another hole for the glass tube which covers the platinum wire ; 
at the edge of the cork cut a nick through which the air can 
pass when the cork is pushed into the tube. TTash the cork 
thoroughly with warm water, and leave it to soak in water for 
some hours before use. Pass the zinc rod about 1 centimetre 
through the cork. 

Contact is made with the mercury by means of a platinum 
wire about Xo. 22 gauge. This is pi-otected from contact 
with the other materials of the cell by being sealed into a 
glass tube. The ends of the wire project from the ends of the 
tube : one end forms the terminal, the other end and a portion 
of the glass tube dip into the mercury. 

Clean the glass tube and platinum wire carefully, then 
heat the exposed end of the platinum red hot, and insert it in 
the mercury in the test tube, taking care that the whole of 
the exposed platinum is covered. 

Shake up the paste and introduce it without contact with 
the upper part of the walls of the test tube, filling the tube 
above the mercury to a depth of rather more than 1 centi- 
metre. 



APPENDIX 581 



Then insert the cork and zinc rod, passing the glass tube 
through the hole prepared for it. Push the cork gently down 
until its lower surface is nearly in contact with the liquid. 
The air will thus be nearly all expelled, and the cell should 
be left in this condition for at least 24 hours before sealing, 
which should be done as follows : 

3Ielt some marine glue until it is fluid enough to pour by 
its own weight, and pour it into the test tube above the cork, 
using sufficient to cover completely the zinc and soldering. The 
glass tube containing the platinum wire should project some 
way above the top of the marine glue. 

The cell may be sealed in a more permanent manner by coat- 
ing the mai'ine glue, when it is set, with a solution of sodium 
silicate, and leaving it to harden. 

The cell thus set up may be mounted in any desirable 
manner. It is convenient to arrange the mounting so that 
the cell may be immersed in a water bath up to the level of, 
say, the upper surface of the cork. Its temperature can then 
be determined more accurately than is possible when the cell is 
in air. 

In using the cell sudden variations of temperature should as 
far as possible be avoided. 

The form of the vessel containing the cell may be varied. In 
the H-form, the zinc is replaced by an amalgam of 10 parts by 
weight of zinc to 90 of mercury. The other materials should be 
prepared as already described. Contact is made with the amal- 
gam in one leg of the cell; and with the mercury in the other, 
by means of platinum wires sealed through the glass. 



Hi 

I 



PROBLEMS AND EXERCISES 



QUESTIONS ON CHAPTER I 

1. In what respects does an electrified body differ from a 
non-electrified body ? 

2. Name some of the different methods of producing electri- 
fication. 

3. A body is charged so feebly that its electrification will 
not perceptibly move the leaves of a gold-leaf electroscope. 
Can you suggest any means of ascertaining whether the charge 
of the body is positive or negative ? 

4. How would you prove that the production of a positive 
charge is accompanied by the production of an eqiial negative 
charge ? 

5. Describe an experiment to prove that moistened thread 
conducts electricity better than dry thread. 

6. Why do we regard the two electric charges produced 
simultaneously by rubbing two bodies together as being of 
opposite kinds? 

7. Explain the action of the electrophorus. Can you sug- 
gest any means for accomplishing by a rotatory motion the 
operations of lifting up and down the cover of the instrument 
so as to obtain a continuous supply instead of an intermittent 
one? 

8. Describe the state of the medium between two oppositely 
charged bodies, and state how you would determine the direc- 
tion of the lines of force at any point. 

9. Explain the Torsion Balance, and how it can be used to 
investigate the laws of the distribution of electricity. 

10. Describe what takes place as an electrified conducting 
ball is made to approach a large conducting surface. Show by 
diagram the direction and relative number of the lines of force. 

582 



PEOBLEMS AND EXERCISES 583 



11 . Two small balls are charged respectively with -f 24 and 
— 8 units of electricity. With what force will they attract one 
another when placed at a distance of 4 centimetres from one 
another? Ans. 12 dynes. 

12. If these two halls are then made to touch for an instant 
and then put back in their former positions, with what force 
will they act on each other ? 

Ans. They will repel one another with a force of 4 dynes. 

13. Enumerate the essential parts of an influence machine ; 
and explain how they operate to produce electrification. 

14. Take the diagrammatic representation of the Wimshurst 
machine (Fig. 40) and fill in the lines of electric force, showing 
their direction and relative number. 

15. Explain the action of the Leyden jar by the consideration 
of electric displacement. 

16. Describe four different ways of electrifying a tourmaline 
crystal. 

17. Zinc filings are sifted through a sieve made of copper 
wire upon an insulated zinc plate joined by a wire to an electro- 
scope. What will be observed ? 

18. Explain the j)rinciple of an air-condenser ; and state why 
it is that the two oppositely charged plates show less signs of 
electrification when placed near together than when drawn apart 
from one another. 

19. There are four Leyden jars A, B, C, and D, of which A, 
B, and D are of glass, C of guttapercha. A, B, and C are of the 
same size, D being just twice as tall and twice as wide as the 
others. A, C, and D are of the same thickness of material, 
but B is made of glass only half as thick as A or D. Compare 
their capacities. 

Ans. Take capacity of A as 1; that of B will be 2; that 
of C will be I ; and that of D will be 4. 

20. How would you show that a bar made half of zinc and 
half of copper is capable of producing electrification? 

21. How would you prove that there is no electrification 
within a closed conductor? 

22. What prevents the charge of a body from escaping away 
at its surface ? 

23. Explain the action of Hamilton's mill. 

24. Two brass balls mounted on glass stems are placed half 
an inch apart. One of them is gradually charged by a machine 
until a spark passes between the two balls. State exactly what 
happened in the other brass ball and in the intervening air up 
to the moment of the appearance of the spark. 



I 



684 ELECTRICITY AND MAGNETISM 



25. Define electric density. A charge of 248 units of elec- 
tricity was imparted to a sphere of 4 centimetres radius. What 
is the density of the charge? Ans. 1-23 (nearly). 



QUESTIONS ON CHAPTER n 

1. A dozen steel sewing-needles are hung in a bunch by 
threads through their eyes. How will they behave when hung 
over the pole of a strong magnet ? 

2. Explain the operation of an iron screen in protecting a 
galvanometer needle from magnets in its vicinity, and state 
why it is not perfectly effectual. 

3. Of what material, and of what shape, would you make a 
magnet which is required to preserve its magnetism unaltered 
for a very long time ? Describe the process of tempering. 

4. What is meant by the resultant magnetic force at a 
point? 

5. Six magnetized sewing-needles are thrust vertically 
through six little floats of cork, and are placed in a basin of 
water with their N-pointing poles upwards. How will they 
affect one another, and what will be the effect of holding over 
them the S-pointing pole of a magnet ? 

6. What distinction do you draw between magnets and mag- 
netic matter ? 

7. On board an iron ship which is laying a submarine tele- 
graph cable there is a galvanometer used for testing the conti- 
nuity of the cable. It is necessary to screen the magnetized 
needle of the galvanometer from being affected by the magnetism 
of the ship. How can this be done ? 

8. How would you prove two magnets to be of equal 
strength ? 

9. The force which a magnet-pole exerts upon another magnet- 
pole decreases as you increase the distance between them. What 
is the exact law of the magnetic force, and how is it proved 
experimentally ? 

10. Describe the behaviour of Ewing's model of molecular 
magnetism in a magnetic field, and show how it corresponds 
with the behaviour of iron when magnetized. Divide the process 
of magnetizing into three successive stages. 

11. What force does a magnet-pole, the strength of which is 
9 units, exert upon a pole whose strength is 16 units placed 6 
centimetres away ? Ans. 4: dynes. 



PROBLEMS AND EXERCISES 585 



12. How would you place a long magnet so that one of its 
poles deflects a compass while the other does not affect it ? 

13. Distinguish between the " strength " of a magnet and its 
" magnetic moment." 

14. Describe an instrument for comparing the relative 
values of magnetic forces. How would you use it to compare 
the magnetic" moments of two magnets? If their distances 
from the magnetometer are respectively 20 centimetres and 30 
centimetres, what is the ratio of their magnetic moments ? 

Ans. 8:27. 

15. Two magnets have the same pole strength, but one is twice 
as long as the other. The shorter is placed 20 centimetres from 
a magnetometer (using the end-on method) ; state at what dis- 
tance" the other must be placed in order that there may be no 
deflexion. Ans. 160 centimetres. 

16. A pole of strength 40 units acts with a force of 32 dynes 
upon another pole 5 centimetres away. What is the strength of 
that pole ? Ans. 20 units. 

17. It is desired to compare the magnetic force at a point 10 
centimetres from the pole of a magnet with the magnetic force 
at 5 centimetres' distance. Describe four ways of doing this. 

18. Explain the phenomenon of Consequent Poles. 

19. In what direction do the lines of magnetic induction 
(or " lines of force ") run in a plane in which there is a single 
magnetic pole? How would you arrange an experiment by 
which to test your answer ? 

20. What is a Magnetic Shell ? What is the law of the poten- 
tial due to a magnetic shell ? 

21. A steel bar magnet suspended horizontally, and set to 
oscillate at Bristol, made 110 complete oscillations in five 
minutes ; the same needle when set oscillating horizontally at 
St. Helena executed 112 complete oscillations in four minutes. 
Compare the horizontal component of the force of the earth's 
magnetism at Bristol with that at St. Helena. 

^ns. H at Bristol: H at St. Helena : : 484: 784. 

22. Supposing the dip at Bristol to be 70^ and that at St. 
Helena to be 30°, calculate from the data of the preceding 
question the total force of the earth's magnetism at St. Helena, 
that at Bristol being taken as 0*48 unit. Ans. 0'307. 

23. A small magnetic needle was placed magnetically north 
of the middle point of a strong bar-magnet which lay (magneti- 
cally) east and west. When the magnet was 3 feet aAvay from 
the needle the deflexion of the latter was 2° : when moved up 



56d ELECTRICITY AND MAGNETISM 



to a distance of 2 feet the deflexion was 6^ 30' ; and when only 1 
foot apart the deflexion was 43^. Deduce the law of the total 
action of one magnet on another. 

24. Describe how the daily irregularities of the earth's mag- 
netism are registered at different stations for comparison. 



QUESTIONS ON CHAPTER III 

1. Show that the total of the differences of potential by con- 
tact in three simple voltaic cells joined in series is three times 
as great as the difference of potential in one cell, the materials 
being the same in each. 

2. Classify the different methods of preventing polarization 
in voltaic cells, and state the advantages and disadvantages of 
using a strong depolarizer, such as chromic acid. 

3. Ou what does the internal resistance of a battery depend ? 
Is there any way of diminishing it ? 

4. A current of 10 amperes flows for half an hour ; find the 
total quantity of electricity that passes. Also define the unit 
by which the quantity is measured. Ans. 18,000 coulombs. 

5. State from what source the energy yielded by a voltaic 
cell is derived. 

6. How is local action in a voltaic cell minimized ? 

7. Twenty-four similar cells are grouped together in four 
rows of six" cells each; compare the electromotive-force and 
the resistance of the battery thus grouped, with the electro- 
motive-force and the resistance of a single cell. 

Ans. The E.M.F. of the battery is six times that of one 
cell. The total internal resistance is one and a half 
times that of one cell. 

8. Describe a form of cell that could be used as a standard 
of E.M.F. State the essential qualities of such a cell. 

9. A piece of silk-covered copper wire is coiled round the 
equator of a model terrestrial globe. Aj^ply Ampere's rule to 
determine in which direction a current must be sent through 
the coil in order that the model globe may represent the condi- 
tion of the earth magnetically. 

A71S. The current must flow across the Atlantic from 
Africa to America, and across the Pacific from 
America toward India ; or, in other words, must flow 
always from east toward west. 

10. A current of "24 amperes flows through a circular coil of 
seventy-two turns, the (average) diameter of the coils being 20 
centimetres. What is the strength of the magnetic field which 
the current produces at the centre of the coil? Ans. 1'08. 



I 



PEOBLEMS AND EXERCISES 587 



11. Show the direction of the lines of force about a conductor 
carrying a current (1) when the conductor is straight ; (2) when 
it is bent into the form of a ring ; (3) when it is wound on a 
cylinder many times round. What do you mean by the direction 
of the lines oi" force ? 

12. Suppose a current passing through the above coil pro- 
duced a deflexion of 35^ upon a small magnetic needle placed 
at its centre (the plane of the coils being in the magnetic meri- 
dian), at a place where the horizontal component of the earth's 
magnetic force is "23 units. Calculate the strength of the current 
in amperes. (Art. 213.) A^is. 0-035. 

13. The current generated by a dynamo-electric machine was 
passed through a large ring of stout copper wire, at the centre 
of which hung a small magnetic needle to serve as a tangent 
galvanometer. When the steam engine drove the armature of 
the generator at 450 revolutions per minute the deflexion of the 
needle was 60^. When the speed of the engine was increased 
so as to produce 900 revolutions per minute the deflexion was 
74°. Compare the strength of the currents in the two cases. 

Ans. The current was twice as great as before, for 
tan 74^ is almost exactly double of tan 60°. 

14. State a general law which will enable you to find the 
way in which the different parts of a magnetic system tend to 
move. 

15. Deduce the law of the force on a magnetic pole due to 
a current flowing along a long straight conductor. 

16. Describe four ways of controlling the needle of a 
galvanometer. 

17. What is meant by a " null method " of observation ? 

18. Why is the needle of a tangent galvanometer made very 
short ? 

19. You are supplied with an ammeter and a voltmeter for 
the purpose of ascertaining the current supplied to an electro- 
lytic bath, and the voltage at which it is supplied. Show how 
you would join them up. 

20. The current from two Grove's cells was passed through 
a sine-galvanometer to measure its strength. When the con- 
ducting wires were of stout copper wire the coils had to be 
turned through 70° before tliey stood parallel to the needle. 
But when long thin wires were used as conductors the coils only 
reqiiired to be turned through 9°. Compare the strength of 
the current in the first case with that in the second case when 
flowing through the thin wires which offered considerable 
resistance. Ans. Currents are as 1 to j, or as 6 to 1. 



I 



588 ELECTRICITY AND MAGNETISM 



21. A plate of zinc and a plate of copper are respectively- 
united by copper wires to the two screws of a galvanometer. 
They were then dipped side by side into a glass containing 
dilute sulphuric acid. The galvanometer needle at first showed 
a deflexion of 28°, but five minutes later the deflexion had 
fallen to 11°. How do you account for this falling off ? 

22. Classify liquids according to their power of conducting 
electricity. In which class would melted pewter come ? 

23. Name the substances produced at the anode and kathode 
respectively during the electrolysis of the following substances : 
— Water, dilute sulphuric acid, sulphate of copper (dissolved 
in water), hydrochloric acid (strong), iodide of potassium (dis- 
solved in water) , chloride of tin (fused) . 

24. A current is sent through three electrolytic cells, the 
first containing acidulated water, the second sulphate of copper, 
the third contains a solution of silver in cyanide of potassium. 
How much copper will have been deposited in the second cell 
while 2 '268 grammes of silver have been deposited in the third 
cell ? And what volume of mixed gases will have been given off 
at the same time in the first cell? 

Ans. •6656 grammes of copper and 351*4: cubic centi- 
metres of mixed gases. 

25. A current passes by platiniTm electrodes through three 
cells, the first containing a solution of blue vitriol (cupric sul- 
phate), the second containing a solution of green vitriol (ferrous 
sulphate), the third containing a solution of ferric chloride. 
State the amounts of the different substances evolved at each 
electrode by the passage of 1000 coulombs of electricity. 

^«9 7r,><s^ rpJJ I Anode "0829 gramme of oxj^gen gas. 
Ans.J^irst Leu, j kathode -3281 gramme of copper. 
i^Prand CpII S Anode "0829 gramme of oxygen. 
becond LeU, j Kathode -2902 gramme of iron. 
,77, .; ^ ,7 ( Anode -3673 gramme of chlorine. 
Liiva oe«, I Kathode -1935 gramme of iron. 

26. The ends of a coil of fine insulated wire are connected 
with the terminals of a galvanometer. A steel bar magnet is 
pushed slowly into the hollow of the coil and then withdrawn 
suddenly. What actions will be observed on the needle of the 
galvanometer ? 

27. Round the outside of a deep cylindrical jar are coiled 
two separate pieces of fine silk-covered wire, each consisting of 
many turns. The ends of one coil are fastened to a battery, 
those of the other to a sensitive galvanometer. "When an iron 
bar is poked into the jar a momentary current is observed in the 
galvanometer coils, and when it is drawn out another momen- 
tary current, but in an opposite direction, is observed. Explain 
these observations. 



PEOBLEMS AND EXERCISES 



28. A casement window has an iron frame. The aspect is 
north, the hinges being on the east side. What happens in the 
frame when the window is opened ? 

29. Explain the construction of the induction coil. What are 
the particular uses of the condenser, the automatic break, and 
the iron wire core? 

30. It is desired to measure the strength of the field between 
the poles of an electromagnet which is excited by a current 
from a constant source. How could you apply Faraday's dis- 
covery of induction-currents to this purpose ? 

31. A small battery was joined in circuit with a coil of fine 
wire and a galvanometer, in which the current was found to 
produce a steady but small deflexion. An uumagnetized iron 
bar was now plunged into the hollow of the coil and then 
withdrawn. The galvanometer needle was observed to recede 
momentarily from its first position, then to return and to 
swing beyond it with a wider arc than before, and finally to 
settle down to its original deflexion. Explain these actions, 
and state what was the source of the energy that moved the 
needle. 

32. A tangent galvanometer, whose "constant" in absolute 
units was 0"08 was joined in circuit with a battery and an 
electrolytic cell containing a solution of silver. The current 
was kept on for one hour ; the deflexion observed at the 
beginning was 36°, but it fell steadily during the hour to 34°. 
Supposing the horizontal component of the earth's magnetic 
force to be "23, calculate the amount of silver deposited in the 
cell during the hour, the absolute electro-chemical equivalent of 
silver being 0"01134. Ans. 0'526 gramme. 

33. A piece of zinc, at the lower end of which a piece of 
copper wire is fixed, is suspended in a glass jar containing a 
solution of acetate of lead. After a few hours a deposit of lead 
in a curious tree-like form ('Arbor Saturni") grows downwards 
from the copper wire. Explain this. 

34. Explain the conditions under which electricity excites 
muscular contraction. How can the converse phenomenon of 
currents of electricity produced by muscular contraction be 
shown ? 

35. A certain piece of apparatus has two terminals on each 
side. To these a pair of wires, A and B, are attached at one 
side, and another pair at C and D. Examination with a volt- 
meter shows that the potential of A is higher than that of B, 
and that of C higher than that of D. Yet examination with an 
ampere-meter shows that a current is flowing from B to A 
through the apparatus, and another current from C to D 
through the other part of the apparatus. By which circuit is 
the energy coming in, and by which is it going out? 



590 ELECTRICITY AND MAGNETISI^I 



36. Show that if N magnetic lines are withdrawn from a cir- 
cuit of resistance E, the quantity of electricity thereby trans- 
ferred aroimd the circuit {i.e. tlie time integral of the induced 
current) wiU be Q = N/R. (See Art. 22.5.) 

37. The strength of the field between the poles of a large 
electromagnet was determined by the following means : — A 
small circuhxr coil, consisting of 40 turns of fine insulated wire, 
mounted on a handle, was connected to the terminals of a 
long-coil galvanometer ha^i-ug a heaAnr needle. On inverting 
tliis coil suddenly, at a place where the total intensity of the 
earth's magnetic force was ••±8 unit, a deflexion of 6^ was shown 
as the first swing of the galvanometer needle. The sensitiveness 
of the galvanometer was then reduced to ihs by means of a 
shunt. The little coil was introduced between the poles of the 
electromagnet and suddenly inverted, when the first swing of 
the galvanometer needle reached iO^. What was the strength 
of the field between the poles ? Ans. 315 '7 units. 



QUESTIONS ON CHAPTER IV 

1. Define the unit of electricity as derived in absolute terms 
from the fundamental units of length, mass, and time. 

2. At what distance must a small sphere charged with 28 
units of electricity be placed from a second sphere charged Ts-ith 
56 units in order to repel the latter with a force of 32 dynes ? 

Ans. 7 centimetres. 

3. Suppose the distance from the earth to the moon to be (in 
round numbers) 383 X 108 centimetres ; and that the radius of 
the earth is 66 X 10" centimetres, and that of the moon 15 x 10" 
centimetres ; and that both moou and earth are charged until 
the surface density on each of them is of the average value of 
10 units per square centimetre. Calculate the electrostatic re- 
pulsion between the moon and the earth. 

4. A small sphere is electrified with 24 units of + electricity. 
Calculate the force with which it repels a unit of + electricity 
at distances of 1, 2, 3, 4, 5, 6, 8, and 10 centimetres respectively. 
Then plot out the ''curve of force " to scale; measuring the 
respective distances along a line from left to right as so many 
centimetres from a fixed point as origin ; then setting out as 
vertical ordiuates the amounts you have calculated for the cor- 
responding forces; lastly, connecting by a curved line the 
system of points thus found. 

5. Define electrostatic (or electric) ''potential" ; and calcu- 
late (by the rule given in italics in Art. 263) the potential at a 
point A, which is at one corner of a square of 8 centimetres' 
side, when at the other three corners B, C, D, taken in order, 
charges of +16, +34, and +24 units are respectively placed. 

A71S. 8 (very nearly) . 



PEOBLEMS AND EXERCISES 591 



6. A small sphere is electrified with 24 units of + electricity. 
Calculate the potential due to this charge at points 1, 2, 3, 4, 5, 
6, ^, and 10 centimetres' distance respectively. Then plot out 
the " curve of potential " to scale, as described in question 4. 

7. A small sphere charged with 100 units of electricity is 
dipped into a bath of oil having a dielectric capacity 2 ; find the 
force it would exert on a unit charge 5 centimetres away. 

Ans. 2 dynes. 

8. Distinguish between the surface density at a point and 
the potential at that point due to neighbouring charges. 

9. What are equipotential surfaces? Why is the surface 
of an insulated conductor an equipotential surface? Is it 
always so ? 

10. Show that the capacity of an isolated sphere in air of 
radius i' has a capacity equal to »' units. What is the electro- 
static unit of capacity ? 

11. Why is the potential of the earth due to charges that we 
produce practically equal to zero ? 

12. A sphere whose radixts is 14 centimetres is charged until 
the surface density has a value of 10. What quantity of electri- 
city is required tor this? Ans. 24,040 units (nearly). 

13. In the above question what will be the potential at the 
surface of the sphere ? (See Art. 269.) ulns. 1760 (very nearly) . 

14. In the case of question 12, what will be the electric force 
at a point outside the sphere and indefinitely near to its sur- 
face? (Art. 276.) ^ns. 125-7 (very nearly) . 

15. Suj)pose a sphere whose radius is 10 centimetres to be 
charged with 6284 units of electricity, and that it is then caused 
to share its charge with a non-electrified sphere whose radius is 
15 centimetres, what will the respective charges and surface- 
densities on the two spheres be when separated ? 

Ans. Small sphere, q =2513*6, 5=2: 
Large sphere, q = 3770-4, ? = 1-33. 

16. A charge of -|- 8 units is collected at a point 20 centi- 
metres distant from the centre of a metallic sphere whose radius 
is 10 centimetres. It induces a negative electrification at the 
nearest side of the sphere. Find a point inside the sphere such 
that if 4 negative units were placed there they would exercise a 
potential on all external points exactly equal to that of the 
actual negative electrification. (See Art. 275.) 

Ans. The point must be on the line between the outside 
positive charge and the centre of the sphere and at 5 
centims. from the surface. 

17. Two large parallel metal plates are charged both posi- 
tively but unequally, the density at the surface of A being + 6, 



592 ELECTRICITY AND MAGNETISM 



that at the surface of B being + 3. They are placed 2 centi- 
metres apart. Find the force Trith Tvhich a + unit of electricity 
is urged from A towards B. Find also the work done by a -j- 
unit of electricity in passing from A to B. 

Ans. Electric force from A tOTvards B = 18*85 dynes : work 
done by unit in passing from A to B = 37'5 e/-gs. 

18. What is meant by the dimensions of a physical quantity? 
Deduce from the Law of Liverse Squares the dimensions of 
electricity ; and show by this means that electricity is not a 
quantity of the same physical dimensions as either matter, 
energy, ov force. 

19. Explain the construction and principles of action of the 
quadrant electrometer. How could this instrument be made 
self-recording ? 

20. Describe the construction of an electrostatic voltmeter, 
and state some of the advantages that this instrument pos- 



21. One of the two coatings of a condenser is put to earth, 
to the other coating a charge of 5400 units is imparted. It is 
found that the difference of potential thereby produced between 
the coatings is 15 (electrostatic) units. "What was the capacity 
of the condenser? Ans. 360. 

22. What is the meaning of specific, inductive, capacity? 
Why does hot glass appear to hare a higher specific inductive 
capacity than cold glass ? 

23. Describe a method of mapping out the lines of force in 
an electrostatic field. 

24. Two condensers of capacity 4 and 6 respectively are 
placed in parallel; and in series with them is placed another 
condenser having a capacity of 5 microfarads. Find the 
capacity of the whole combination. Ans. 3-3. 

25. Compare the phenomenon of the residual charge in a 
Leyden jar with the phenomenon of polarization in an electro- 
lytic cell. 

26. A condenser was made of two flat square metal plates, 
the side of each of them being 35 centimetres. A sheet of 
indiarubber -4 centim. thick was placed between them as a 
dielectric. The specific inductive capacity of indiarubber being 
taken as 2*25, calculate the capacity of the condenser. 

Ans. 548*8 electrostatic units. 

27. Calculate (in electrostatic units) the capacity of a mile 
of telegraph cable, the core being a copper wire of "18 centim. 
diameter, surrounded by a sheathing of guttapercha "91 centim. 
thick. \k for guttapercha = 2*46 : one mile = 160,933 centims.] 

Ans. 82,164 units. 



PROBLEMS AND EXERCISES 593 



28. A Leyden jar is made to share its charge with two other 
jars, each of which is equal to it in capacity. Compare the 
energy of the charge in one jar with the energy of the original 
charge. Ans. One ninth as great. 

29. A series of Leyden jars of equal capacity are charged 
"in cascade." Compare the total energy of the charge of the 
individual jars thus charged, with that of a single jar charged 
from the same source. 

30. Classify the various modes of discharge, and state the 
conditions under which they occur. 

31. Suppose a condenser, whose capacity is 10,000 charged 
to potential 14, to he partially discharged so that the potential 
fell to 5. Calculate the amount of heat produced by the 
discharge, on the supposition that all the energy of the spark 
is converted into heat. Ans. '020357 of a unit of heat. 

32. How do changes of pressure affect the passage of electric 
sparks through air ? 

33. Describe some of the properties of matter in its ultra- 
gaseous or radiant state. 

34. Why are telegraphic signals through a submerged cable 
retarded in transmission, and how can this retardation be 
obviated ? 

35. How is the difference of potential between the earth and 
the air above it measured? and what light do such measure- 
ments throw on the periodic variations in the electrical state of 
the atmosphere ? 

36. What explanation can be given of the phenomenon of 
a thunderstorm ? 

37. What are the essential features which a lightning-con- 
ductor must possess before it can be pronounced satisfactory ? 
And what are the reasons for insisting on these points ? 



38. How can the duration of an electric spark be measured 



QUESTIONS ON CHAPTER V 

1. Define magnetic potential, and find the (magnetic) potential 
due to a bar magnet 10 centimetres long, and of strength 80, at 
a point lying in a line with the magnet poles and 6 centimetres 
distant from its N-seeking end. Ans. 8*3. 

2. A N-seeking pole and a S-seeking pole, whose strengths 
are respectively + 120 and — 60, are in a plane at a distance of 
6 centiiiietres apart. Find the point between them where the 
potential is = ; and through this point draw the curve of zero 
potential in the plane. 

2q 



594 ELECTRICITY AND MAGNETIS^I 



3. Define " iuteusity of the magnetic field." A magnet 
whose strength is 270 is placed in a uniform magnetic field 
whose intensity is '16Q. What are the forces which act upon its 
poles? Ans. -\- io dynes aud — 45 dynes. 

4. Define "intensity of magnetization." A rectangular 
bar-magnet, whose length was 9 centimetres, was magnetized 
until the strength of its poles was 16-4. It was 2 centimetres 
broad aud "5 centimetre thick. Supposing it to be uniformly 
magnetized throughout its length, what is the intensity of the 
magnetization? Ans. 164. 

5. A certain electric motor has 100 conductors on its arma- 
ture, each carrying 10 amperes. The number of lines of force 
passing throug-h the armature is 500,000, Find the work (in 
ergs) done in one revolution of the armature. 

As each conductor cuts the lines twice in one revolution the 
answer will be 100,000,000 ergs. 

6. Find the torque (see Art. 136) on the armature described 
in the last question. Note that with the above data the torque 
is independent of the radius of the armature, for the force on 
each conductor is proportional to the strength of the field, and 
this is inversely proportional to the radius if N remains the 

Ans. mmm dyne-cenUmetres. 

In 

7. A current whose strength in " absolute " electromagnetic 
units was equal to 0*05 traversed a wire ring of 2 centimetres 
radius. "VMiat was the strength of field at the centre of the 
ring ? What was the potential at a point P opposite the middle 
of the ring and 4 centimetres distant from the circumference of 
the ring? Ans.f^ -1571 ; Y = ± 00421. 

8. (a) A spiral of wire of 1000 turns carries a current of 1 
ampere. Find the total magnetomotive force which it exerts. 

Ans. 1257. 

(6) If the spiral were 1 metre in length and 1 centimetre in 
diameter, find the force on a unit pole placed (1) in its centre; 
(2) at its end. Ans. 12'57 dynes and 6-28 dynes. 

9. What limits are there to the power of an electromagnet ? 

10. What is the advantage in using an iron core in an electro- 
magnet ? 

11. A rod of soft iron, 0'32 cm. in diameter and 1 metre long 
is uniformly overwound from end to end with an insulated 
copper wire making 637 turns in one layer. Find (using Bid- 
well's data in Art. 365) what strength of poles this rod will 
acquire when a current of 5 amperes is sent through the coil. 

Ans. 386 units. 



J 



PROBLEMS AND EXERCISES 595 



12. Enunciate Maxwell's rule concerning magnetic shells, 
and from it deduce the laws of parallel and oblique currents 
discovered by Amj)ere. 

13. A circular copper dish is joined to the zinc pole of a 
small battery. Acidulated water is then poured into the 
dish, and a wire from the carbon pole of the liattery dips into 
the liquid at the middle. A few scraps of cork are thrown 
in to render any movement of the liquid visible. What will 
occur when the N-seeking pole of a strong bar-magnet is held 
above the dish ? 

14. Roget hung up a spiral of copper wire so that the lower 
end just dipped into a cup of mercury. When a strong current 
was sent through the spiral it started a continuous dance, the 
lower end producing bright sparks as it dipped in and out of 
the mercury. Explain this experiment. 

15. It is believed, though it has not yet been proved, that 
ozone is more strongly magnetic than oxygen. How could this 
be put to proof ? 

16. What is meant by the permeability of a substance? 
State some substances in which it is constant, and some in 
which it varies. 

17. Describe a method of measuring the permeability of 
iron. 

18. A ring of iron is wound with two coils. One coil is 
connected to a ballistic galvanometer, and on connecting the 
other to a battery a throw of the needle of 160 scale divisions 
is observed. The current is then broken and there is a throw 
of 40 divisions in the opposite direction. Why are the two 
throws not equal ? What change has taken place in the iron ? 
How would you bring it back to its original condition ? 

19. Sketch a closed hysteresis curve for hard steel, for 
which, when H is raised to 100, B = 12,800, and for which the 
remanence is 9500 and the coercive force 40. 

20. An iron bar 30 centimetres long and 10 square centi- 
metres in sectional area is bent into the shape of a horse-shoe 
for the purpose of making an electromagnet which shall have 
a pull of 66 kilograms upon its armature (a bar 12 centimetres 
long and 10 square centimetres in section) when it is 2 inch 
away from its poles. Find the number of ampere turns 
required, assuming a leakage of one-third of the lines of force. 

Taking the formula : — 

— X 20 sq. cms. of pole face = 66,000 X 981 dynes, 

8n 

we get B = 9000. From the table, Art. 364, mi for the armature 



I 



696 ELECTRICITY AND MAGNETISM 



= 2250, B for the horse - shoe = 1-5 x 9000 = 13,500, so that 
/x., = 900, then ampere-turns = 

90,000 I _^2_ 1:5_X30 ^ 2x0-5 X 2-51 ) ^1.257 = 18,930. 
(10X2250^10X900 10 i 

21. What thickness of copper wire must be used to wind the 
above magnet in order to obtain 18,930 ampere turns, the wind- 
ing on each cylindrical bobbin ha^ang a mean diameter of 7 
centimetres, if the pressure at the terminals of the magnet is 
intended to be 100 volts ? 

If r is the resistance of one turn, and s the number of turns, 
r = ^ = _M^ ; but we know that r = X>liL x 1-6 X 10-6. 

CS 18,930 CP X i;r 



Hence diameter of wire, d = ^/ -^"'-^"^^ ' ^ j^ ^ -^ ^j ^ 9'092 



18,930 X 7 X 4 X 1-6 
cms. '" " \ 106x100 

N.B. — The thickness of wire is independent of the number 
of turns (except in so far as this affects the mean diameter of 
the bobbin), but the greater the number of turns the less will be 
the number of watts expended. 

22. "What is the object of "polarizing" the armature of a 
magnet in a piece of mechanism , such as a relay ? 

23. Describe the construction of a current-balance, and the 
mode of using it. 

QUESTIONS ON CHAPTER VI 

1. The resistance of telegraph wire being taken as 13 oJims 
per mile, and the E.M.F. of a Leclanclie cell as l"-± volt, calculate 
how many cells are needed to send a current of 12 milli-amperes 
through a line 120 miles long ; assuming that the instruments in 
circuit offer as much resistance as 20 miles of wire would do, 
and that the return current through eca^th meets with no appre- 
ciable resistance. Ans. 16 cells. 

2. Fifty Grove's cells (E.M.F. of a Grove = 1-8 volt) are imited 
in series, and the circuit is completed by a wire whose resistance 
is 15 ohms. Supposing the internal resistance of each cell to be 
0'3 ohm, calculate the strength of the current. 

Ans. 3 amperes. 

3. The current running through an incandescent filament of 
carbon in a lamp was found to be exactly 1 ampere. The differ- 
ence of potential between the two terminals of the lamp while 
the current was flowing was found to be 30 volts. What was 
the resistance of the filament ? 

4. Define specific resistance. Taking a specific resistance of 
copper as 1642, calculate the resistance of a kilometre of copper 
wire whose diameter is 1 millimetre. Ans. 20"9 ohms. 



PEOBLEMS AND EXERCISES 597 



o. On measuring the resistance of a piece of No. 30 B. W. G. 
(covered) copper wire, 18'12 yards long, I found it to have a 
resistance of 3"02 ohms. Another coil of the same wire had a 
resistance of 22-65 ohms ; what length of wire was there in the 
coil ■? Ans. 135'9 yards. 

6. Calculate the resistance of a copper conductor one square 
centimetre in area of cross-section, and long enough to reach 
from Niagara to New York, reckoning this distance as 480 
kilometres. Ayis. 78'8 ohms. 

7. Find the di'op in volts if 400 amperes is passed through 
this conductor. What would be the waste of power (in loatts)? 

Ans. 31,520 volts, 12,608,000 ivatts. 

8. The resistance from plate to plate in a certain electrolytic 
bath is 0*9 of an ohm. You wish to pass through it the 
strongest current you can get from 20 Daniel 1 cells, each with 
a resistance of one ohm. How would you group the cells? 

Ans. 4 in series, 5 rows in parallel. 

9. The specific resistance of guttapercha being 3*5 X 10^3, 
calculate the number of coulombs of electricity that would 
leak in one century through a sheet of guttapercha one centi- 
metre thick and one metre square, whose faces were covered 
with tinfoil and joined respectively to the poles of a battery of 
100 Daniell's cells. Ans. 9*7 coulombs. 

10. Six Daniell's cells, for each of which E = 1-05 volt, r = 
O'o ohm, are joined in series. Three wires, X, Y, and Z, whose 
resistances are severally 3, 30, and 300 ohms, can be inserted 
between the poles of the battery. Determine the current which 
flows when each wire is inserted separately ; also determine 
that which flows when they are all inserted at once in parallel. 

Ans. Through X 1*05 amperes. 

Through Y 0-1909 

Through Z 0-0207 " 

Through all three 1*105 

11. Calculate the number of cells required to produce a cur- 
rent of 50 milU-amperes through a line 114 miles long, whose 
resistance is 12| ohms per mile, the available cells of the bat- 
terv having each an internal resistance of 1-5 oh^n, and an 
E.M.F. of 1-5 volt. Ans. 50 cells. 

12. You have 20 large Leclanche cells (E.M.F. = 1-5 volt, r = 
0-5 ohm each) in a circuit in which the external resistance is 10 
ohms. Find the strength of current which flows (a) when the 
cells are joined in simple series; (6) all the zincs are united, 
and all the carbons united, in parallel arc; (c) when the cells 
are arranged two abreast [i.e. in two files of ten cells each) ; 
{d) when the cells are arranged four abreast. 

Ans. (a) 1-5; (&) 0-1496; (c) 1-2; {d) 0-702 ampere. 



598 ELECTRICITY AND MAGNETISM 



13. With the same battery how would you arrange the cells 
in order to telegraph through a line 100 miles long, reckoning 
the line resistance as 12^ ohms per mile ? 

14. Show that, if we have a battery of n given cells each of 
resistance r in a circuit where the external resistance is R, the 
strength of the current will be a maximum when the cells are 
co upled up in a certain number of rows equal numerically to 
Vnr -f- R. 

15. Two wires, whose separate resistances are 28 and 24, 
are placed in parallel in a circuit so that the current divides, 
part passing through one, part through the other. What 
resistance do they offer thus to the current ? 

Ans. 12"92 ohms. 

16. Using a large bichromate cell of practically no internal 
resistance, a deflexion of 9" was obtained upon a tangent gal- 
vanometer (also of small resistance) through a wire whose 
resistance was known to be 435 ohms. The same cell gave a 
deflexion of 5"^ upon the same galvanometer when a wire of 
unknown resistance was substituted in the circuit. What was 
the unknown resistance ? Ans. 790 ohms. 

17. In a Wheatstone's bridge, in which resistances of 10 and 
100 ohms respectively were used as the fixed resistances, a wire 
whose resistance was to be determined was placed : its resist- 
ance was balanced when the adjustable coils were arranged to 
throw 281 ohms into circuit. What was its resistance? 

Ans. 28-1 ohms. 

18. Describe the method of using a metre bridge to measure 
resistances. 

19. Give the proof of Foster's method of measui'ing small 
differences of resistance from the consideration of Ohm's law. 

20. To find the voltage of a djoiamo you connect to its 
brushes the ends of a German-silver wire 120 feet long, wound 
on an insulating cylinder, and find that when one terminal of 
a Daniell cell (1"05 volt) is joined to a point on the wire, and 
the other terminal in series with a galvanometer is connected 
to another point 1 ft. from the first, no deflexion is observed. 
What is the voltage of the dynamo ? A7is. 126 volts. 

21. A battery of 5 Leclanche cells was connected in simple 
circuit with a galvanometer and a box of resistance coils. A 
deflexion of 39° having been obtained by adjustment of the 
resistances, it was found that the introduction of 150 addi- 
tional ohms of resistance brought down the deflexion to 22°. 
Assuming the galvanometer to have 140 ohms resistance, find 
the internal resistance of the battery. Ans. 10 ohms. 

22. How are standard resistance coils wound, and why? 
What materials are they made of, and why ? 



PROBLEMS AND EXERCISES 599 



23. Three very small Daniell's cells gave, with a sine gal- 
vanometer (itself of no appreciable resistance), a reading of 
57^. On throwing 20 ohms into the circuit the galvanometer 
reading fell to 25^. Calculate the internal resistance of the 
cells. Ans. 6*6 ohms each. 

24. A length of telegraph cable was plunged in a tub of 
water and fhen charged for a minute from a battery of 120 
Daniell's cells. The cable was then discharged through a long- 
coil galvanometer with a needle of slow swing. The first swing 
was 40=". A condenser whose capacity was 3 microfarad was then 
similarly charged and discharged; but this time the first swing 
of the needle was only 14°. What was the capacity of the piece 
of cable ? Ans. 0*934 microfarad. 

25. Using an absolute electrometer. Lord Kelvin found the 
difference of potential between the poles of a Daniell's cell to 
be 0*00374 electrostatic units (C.G.S. system). The ratio of the 
electrostatic to the electromagnetic unit of potential is given 
in Art. 359, being = 1/v. The volt is defined as 10^ electromag- 
netic units. From these data calculate the E.M.F. of a Daniell's 
cell in volts. Ans. 1-115 volt. 

26. The radius of the earth is approximately 63 X lO'' centi- 
metres. The ratio of the electrostatic to the electromagnetic 
unit of capacity is given in Art. 359. The definition of the 
farad is given in Art. 354. Calculate the capacity of the 
earth (regarded as a sphere) in microfarads. 

Ans. 700 microfarads (nearly). 

27. The electromotive-force of a Daniell's cell was deter- 
mined by the following process : — Five newly-prepared cells 
were set up in series with a tangent galvanometer, whose 
constants were found by measurement. The resistances of the 
circuit were also measured, and found to be in total 16'9 ohms. 
Knowing the resistance and the absolute strength of current 
the E.M.F. could be calculated. The deflexion obtained was 
45^, the number of turns of wire in the coil 10, the average 
radius of the coils 11 centimetres, and the value of the hori- 
zontal component of the earth's magnetism at the place was 
0-18 G.C.S. units. Deduce the E.M.F. of a Daniell's cell. 

Ans. 1-0647 X 10^ G.C.S. units, or 1-0647 volt. 

28. Apply the formula of the ballistic galvanometer (Art. 
418, h) to determine the number of magnetic lines cut by an 
exploring coil (Art. 366, 6) when the magnetism in the core 
on which it is wound is suddenly reversed. If R is the resist- 
ance of the circuit, Q = 2N/R. Hence the answer is N = RT 
sin ia/2TrS, where S is the number of turns in the exploring 
coil. 

29. Suppose a copper disk to revolve in a field produced by 
a fixed coil closely surrounding its circumference. In circuit 
with the coil is a small battery and a resistance wire. In the 



600 ELECTRICITY AND MAGNETISM 



wire are found two points such that the fall of potential between 
them is equal to the volts generated between the centre and 
circumference of the revolving disk. By balancing these with 
a galvanometer Lorenz was able to calculate in absolute meas- 
ure the resistance of the wire. If M be the coefficient of mutual 
induction between the circumference of the disk and the sur- 
rounding coil, and T the period of revolution of the disk, show 
that R the resistance between the points = M-^- T. 

Ans. Since N the magnetic flux through the disk = MC, 
and E = N/T, and C = E/R, it follows that CR = 
MC/T, whence R = M/T. q.e.d. 



QUESTIONS ON CHAPTER Vn 

1. A strong battery-current is sent, for a few moments, 
through a bar made of a piece of antimony soldered to a piece 
of bismuth. The battery is then disconnected from the wires 
and they are joined to a galvanometer which shows a de- 
flexion. Explain this phenomenon. 

2. A long strip of zinc is connected to a galvanometer by 
iron wires. One junction is kept in ice, the other is plunged 
into water of a temperature of 50° C. Calculate, from the table 
given in Art. 422, the electromotive-force which is producing 
the current. Ans. 690 microvolts. 

3. When heat is evolved at a junction of two metals by the 
passage of a current, how would you distinguish between the 
heat due to resistance and the heat due to the Peltier effect ? 

4. Lord Kelvin discovered that when a current flows through 
iron it absorbs heat when it flows from a hot point to a cold 
point ; but that when a current is flowing through copper it 
absorbs heat when it flows from a cold point to a hot point. 
From these two facts, and from the general law that energy 
tends to run down to a minimum, deduce which way a current 
will flow round a circuit made of two half-rings of iron and 
copper, one junction of which is heated in hot water and the 
other cooled in ice. 

5. Give a curve showing the increase and decrease of the 
thermo-electromotive-force as a junction of iron and copper is 
raised from 0° C. to 400° C, and explain it by means of the 
thermo-electric diagram of Professor Tait. 



QUESTIONS ON CHAPTER VIII 

1. Calculate by Joule's law the number of calories developed 
in a wire whose resistance is 4 ohms when a steady current of 
0*14 ampere is passed through it for ten minutes. 

Ans. 11'2 calories. 



PROBLEMS AND EXERCISES 601 



2. Why does the platinum wire in a Cardew voltmeter, 
when a steady voltage is applied to it, rise to a certain tem- 
perature and then remain at that temperature without altera- 
tion? 

3. Show from the definitions of the horse-power and of the 
watt, and from the relations between the pound and the gramme, 
the foot and the centimetre, that there are 746 watts in one 
horse-power. 

4. Explain why you would expect the heat produced in a 
conductor to be proportional to the square of the current. 

5. Describe the construction of a watt meter and explain 
how you would connect it up to measure the power supplied to 
an electric motor. 

6. Explain why it is advantageous to distribute electric 
energy at a high voltage. There is already laid a copper main 
having a resistance of 0'5 of an ohm along which it is desired to 
transmit 4 kilowatts, and to deliver it at the far end at a pressure 
of 100 volts. Which would be the more efficient method of the 
two following, to send 40 amps, at an initial pressure of 120 volts, 
or to send a current at a pressure of 2400 volts, using a trans- 
former with an efficiency of 85 per cent ? 

Atis. The latter method would, have an efficiency of 84"9 
per cent, the former of 83*3 per cent. 

7. Mention some of the principles upon which supply meters 
have been designed. 

8. An electric motor is supplied at a pressure of 100 volts : 
the armature resistance is 001 ohm. When it is supplying 20 
horse-power, what is its electrical efficiency? 

Ans. 98'5 per cent. 

9. Show under what circumstances an electric motor is most 
efficient. 

10. Enumerate the principal parts of an arc lamp. 

11. Why in a continuous-current arc lamp is the current 
usually sent downwards rather than upwards ? 

12. Why does the filament of an incandescent lamp get 
hotter than the platinum leading-in wires ? 

13. Explain by a diagram the system of three-wire dis- 
tribution ; and point out its advantage over a two-wire distri- 
bution. 

14. A current of 9 amperes worked an electric arc light, and 
on measuring the difference of potential between the two car- 
bons by an electrometer it was found to be 50 volts. What was 
the amount of horse-power absorbed in this lamp ? 

A71S. 0'603 horse-power. 



602 ELECTRICITY AND MAGNETISM 



QUESTIONS ON CHAPTER IX 

1. The reluctance of the core of a certain transformer is 
0*002. Find the coefficient of mutual induction between the 
primary and secondary coils which have 1000 and 50 turns 
respectively, assuming no magnetic leakage. 

Ans. 0-628 henry. 

2. A battery current is sent through the primary of this 
transformer. State from Lenz's law the direction (relatively 
to this current) of the E.M.F.'s induced in both the primary 
and secondary, («) when the current is starting, (6) when it is 
ceasing. 

3. Foucault set the heavy bronze wheel of his gyroscope 
spinning between the poles of a powerful electromagnet, and 
found that the wheel grew hot. What was the cause of this ? 
Where did the heat come from ? 

4. You try to turn a copper disk between the poles of a 
magnet. If you move it slowly it goes quite easily, if you try 
to move it quickly it resists. Why is this? What is the force 
required to turn it proportional to ? 

5. The shunt coil of a certain dynamo has a resistance of 
40 ohms. It is switched on to a battery of accumulators yield- 
ing 100 volts, and one second afterwards the current has risen 
to 0*9825 of an ampere. Find the coefficient of self-induction of 
the shunt coil. Assume log 0*607 = t- 783 and log e=r 0*434. 

Ans. 80 henries. 

6. If a battery of 10 cells each of 1*4 volt and 2 ohms 
resistance be applied to a circuit which has a resistance of 5 
ohms and inductance 0*1 henry, find what modes of grouping 
the cells are best {a) to give the largest steady current, (&) to 
give the largest current at the end of toVs second, (c) to give the 
largest amount of external work relatively to the weight of 
zinc consumed. 

Ans. (a) 5 in series, 2 rows in parallel. (&) All in series, 
(c) All in parallel. 



QUESTIONS ON CHAPTER X 

1. What devices are employed in continuous current dy- 
namos to obtain {a) a current continuously in one direction, 
(6) a current of uniform strength? 

2. Apply Fleming's Rule (Art. 226) to determine which 
way the electromotive-forces will operate in a ring armature 



PROBLEMS AND EXERCISES 603 



(gramme) wound right-handedly over the core revolving right- 
handedly in a horizontal magnetic field having the N pole on 
the right hand. 

Ans. The induced E.M.F.'s tend to make the currents 
climb, in both the ascending and descending halves, 
toward the highest point of the ring. 

3. A dynamo's field magnet gives a flux of 9,000,000 lines. 
How many conductors must there be on the armature in order 
that the dynamo may generate 108 volts when driven at a speed 
of (300 revolutions per minute? Atis. 120. 

4. You have an engine which will drive a dynamo at a fairly 
constant speed at all loads. How would you excite the dynamo 
if it were intended for lighting by incandescent lamps ? Make 
a diagrammatic sketch of all necessary connexions, including 
the lamp circuit. 

5. Take the equation E = a sin {2nnt). Let a = 140 and 
n = 100. Now take different values for t, beginning t = '0005 
of a second, then t = -001, taking 20 different values until 
t = -01. Fill in the values in the above equation and find the 
corresponding 20 values of E. Then plot on squared paper 
taking E as ordinate and t as abscissae. The result will be a 
curve like that shown in Fig. 251. 

6. Repeat the process of the last question, taking the equa- 
tion C = & sin {2wnt — <^), where b = 20, n = 100, and = 0-5 
radian. Plot the results upon the same paper as the curve in 
the last equation was plotted. One curve represents the E.M.F. 
at each instant, the other the lagging current. 

7. An alternating pressure of 100 (virtual) volts following 
a sine law with a frequency of 100 per second is applied to the 
ends of a coil having a resistance of 8 ohms and a coefficient of 
self-induction of 0*005 henry ; find the current that will flow and 
the angle of lag. 

Ans. Current = 11*6 amperes ; lag = 22 degrees. 

8. An alternate-current magnet with properly laminated 
core has a coil of 160 turns, and a coefficient of self-induction 
of 0005 of a henry. What alternating voltage of frequency 
100 per second must be applied to it in order to obtain 4800 
ampere-turns, assuming the resistance to be negligible? 

A7ts. 47-1. 

9. How much resistance must be put in circuit with the coils 
of this magnet in order that the angle of lag may be 45° ? 

A71S. 3-14. 

10. An alternate-current transformer is designed to give out 
40 amperes at a pressure of 50 volts at its secondary terminals. 
No. of windings 300 primary; 12 secondary. Resistances 12 



604 ELECTRICITY AND MAGNETISM 



ohms, primary ; 0'014 ohm, secondary. Find the coeflficient of 
transformation, and the volts that must be applied at the pri- 
mary terminals. 

Alls. Coefficient of transformation is 25; volts at pri- 
mary terminals 1283. 

11. State the principles upon which continuous-current trans- 
formers are made. Why is it necessary to have a moving part 
in continuous-current transformers and not in alternate-current 
transformers ? 

12. Enumerate three distinct kinds of alternate-current 
motors, and state which kind is synchronous and which not. 

13. An alternate-current synchronous motor is supplied from 
the street mains. It is found that when fully loaded it takes 
more current than when lightly loaded, though it always goes 
at the same speed and the volts remain constant. Explain how 
this comes about. 

14. How can you produce a rotatory magnetic field ? De- 
scribe some of its properties. 

QUESTIONS ON CHAPTER XI 

1. It is found that a single Daniell's cell will not electrolyze 
acidulated water, however big it may be made. It is found, on 
the other hand, that two Daniell's cells, however small, will 
suffice to produce continuous electrolysis of acidulated water. 
How do you account for this ? 

2. From the table of electro-chemical equivalents (Art. 240) 
calculate how many coulombs it will take to deposit one grain 
of the following metals: — Copper (from sulphate), silver, 
nickel, gold. ■ Ans. Cu 3058, Ag 891, Ni 3286, Au 1473. 

3. A battery of 2 Grove cells in series yields a current of 5 
amperes for 2 hours ; how much zinc will be consumed, assum- 
ing no waste ? j ??.s. 24-26. 

4. Calculate the E.M.F. of a Daniell cell from considerations 
of the heat value of the combinations which take place and the 
quantity of the elements consumed, taking the heat value for 
zinc in sulphuric acid as 1670 and that for copper as 909-5. 

Alls. 1-11 volts. 

5. Describe the construction and working of a modern 
secondary battery. 

6. Most liquids which conduct electricity are decomposed 
(except the melted metals) in the act of conducting. How do 
you account for the fact observed by Faraday that the amount 
of matter transferred through the liquid and deposited on the 
electrodes is proportional to the amount of electricity trans- 
ferred through the liquid ? 



PROBLEMS AND EXERCISES 605 



7. Describe the process for multiplying by electricity copies 
of engraA-iugs on wood-blocks. 

8. How would, you make arrangements for silvering spoons 
of nickel-bronze by electro-deposition ? 



QUESTIONS ON CHAPTER XH 

1. Sketch an arrangement by which a single line of wire 
can be used by an operator at either end to signal to the 
other ; the condition of working being that whenever you are 
not sending a message yourself your instrument shall be in 
circuit with the line wire, and out of circuit with the battery at 
your own end. 

2. What advantages has the Morse instrument over the 
needle instruments introduced into telegraphy by Cooke and 
Wheatstone ? 

3. Explain the use and construction of a relay. 

4. Show, from the law of traction (Art. 384), that the change 
of attracting force resulting from a cliange in the number of 
magnetic lines that enter an armature will be greater if the 
system is polarized {i.e. magnetized to begin with) than if it is 
non-polarized. 

An8. Since /aN^, it follows that / + (?/ will be propor- 
tional to (N-f-(?N)2. Expanding, and subtracting 
the former, and neglecting the small term (c^N)2, we 
find d/a 2N • c?N ; which shows that, for a given (?N, 
df<x N. 

5. It is desirable in certain cases (duplex and quadruplex 
signalling) to arrange telegraphic instruments so that they will 
respond only to currents which come in one direction through 
the line. How can this be done ? 

6. It is wished to make a sort of duplex telegraph by using 
one set of instruments that work with continuous currents, 
the other set with rapidly alternating currents, at the same 
time on the same line. To carry out this idea there must be 
found (a) an apparatus which will let continuous currents 
flow through it, but will choke off alternate currents; (6) an 
apparatus which will transmit alternate currents, but cut off 
continuous currents. What apparatus will do these things ? 

7. A battery is set up at one station. A galvanometer 
needle at a station eighty miles away is deflected through a 
certain number of degrees when the wire of its coil makes 
twelve turns round the needle ; wire of the same quality being- 
used for both line and galvanometer. At 200 miles the same 
deflexion is obtained when twenty-four turns are used in the 
galvanometer-coil. Show by calculation {a) that the internal 



606 ELECTRICITY AND MAGNETISM 



resistance of the battery is equal to that of 40 miles of the 
line-wire; (6) that to produce an equal deflexion at a station 
360 miles distant the number of turns of wire in the galvan- 
ometer-coil must be 40. 

8. Suppose an Atlantic cable to snap off short during the 
process of laying. How can the distance of the broken end 
from the shore end be ascertained ? 

9. Suppose the copper core of a submarine cable to part at 
some point in the middle without any damage being done to the 
outer sheath of guttapercha. How could the position of the 
fault be ascertained by tests made at the shore end ? 

10: Explain the construction and action of an electric bell. 

11. Describe and explain how electric currents are applied 
in the instruments by which very short intervals of time are 
measured. 



QUESTIONS ON CHAPTER XIII 

1. Explain the use of Graham Bell's telephone (1) to 
transmit vibrations; (2) to reproduce vibrations. 

2. Describe a form of telephone in which the vibrations of 
sound are transmitted by means of the changes they produce 
in the resistance of a circuit in which there is a constant 
electromotive-force. 

3. Two coils, A and B, of fine insulated wire, made exactly 
alike, and of the same number of windings in each, are placed 
upon a common axis, but at a distance of 10 inches apart. 
They are placed in circuit with one another and with the second- 
ary wire of a small induction-coil of Ruhmkorff' s pattern, the 
connexions being so arranged that the currents run round 
the two coils in opposite directions. A third coil of fine wire, 
C, has its two ends connected with a Bell's telephone, to which 
the experimenter listens while he places this third coil between 
the other two. He finds that when C is exactly midway be- 
tween A and B no sound is audible in the telephone, though 
sounds are heard if C is nearer to either A or B. Explain 
the cause of this. He also finds that if a bit of iron wire is 
placed in A silence is not obtained in the telephone until C 
is moved to a position nearer to B than the middle. Why 
is this? Lastly, he finds that if a disk of brass, copper, or 
lead is interposed between A and C, the position of silence 
for C is now nearer to A than the middle. How is this 
explained ? 



PROBLEMS AND EXERCISES 607 



QUESTIONS OX CHAPTER XIV 

1. "What apparatus ^-ould you use to prodttce electric oscilla- 
tions? Show how you would operate it, and explain why the 
oscillations take place. 

2. Explain how electric oscillations in a condenser circuit 
produce electric waves in the surrounding medium. 

3. The capacity of an air-condenser is O'OOl of a microfarad. 
It is charged and then discharged through a circuit having a 
seK-induction of O'OOl of a henry and a resistance of 4 ohms. 
Find the frequency of the vibration. Ans. n = 159,100. 

4. Under what circumstances do oscillations not take place 
when a condenser is discharged ? 

5. If the frequency of oscillation of a Hertz oscillator is 
3,000,000 per second, find the length of the waves it will produce. 

Ans. 10,000 centimetres. 

6. Explain the action of a resonator. 

7. Give the reasons which exist for thinking that light is an 
electromagnetic phenomenon. 

8. How is the action of magnetic forces upon the direction 
of the vibrations of light show^n? and what is the difference 
between magnetic and diamagnetic media in respect of their 
magneto-optic properties ? 

9. It was announced by Willoughby Smith that the resist- 
ance of selenium is less when exposed to light than in the dark. 
Describe the apparatus you would employ to investigate this 
phenomenon. How would you proceed to experiment if you 
wished to ascertain whether the amount of electric effect was 
proportional to the amount of illumination ? 



I 



INDEX 



N.B. — The Xumbers refer to the J^umbered Paragraphs. 



ABSOLrxE Electrometer, 28T 

Galvanometer, 213 

units, 353 
Accumulators, 492 (see also Con- 
denser) 

used in locomotion, 4i6 
Action at a distance, 25, 64, 299 

in medium, 5, 13, 64, 279, 299 
Aether (see Ether) 
Air condenser, 56, 294, 859 
Air-gap, 3TS 

Air, resistance of, 313, 826 
Aldini, Giovanni, experiments on 

Animals, 255 
Alternate currents, 162, 461, 470 
Alternate current magnet, 388, 477 

method of measuring resist- 
ance, 417 

motors, 484 

power, 475 
Alternators, 478 
Aluminium, reduction of, 494 
Amalgam, electric, 44 

ammonium-, sodium-, etc., 490 
Amalgamating zinc plates, 174 
Amber, 2 

Amoeba, the sensitiveness of, 256 
Ammeter, 221 

Ampere, Andre Marie, Theory of 
Electro-dynamics, 392 

''Ampere's E\i\e,'' 197, 382 

Laws of currents, 390, 391 

suggest a Telegraph, 497 

Table for Experiments, 391 

Theory of Magnetism, 898 
Ampere, the, 162, 207, 354 

meter, 221 
Ampere-turns, 341, 377 (and p. 595) 



Amplitude of E.M.F., 470 
Angle of lag, 472, 473 
Angles. Ways of Eeckoning, 144, 
Appendix A 

Solid, 148, Appendix A 
Animal Electricity, 76, 257 
Anion, 239, 491 

Annual variations of magnet, 157 
Anode, 170, 236 
Anomalous magnetization, 373 
Aperiodic galvanometer, 219 
Apparent watts, 438, 472, 475 

resistance, 417e, 458c, 472 
Appropriating brush, 50 
Arago, Franqois Jean, 

classilication of lightning, 
331 

on magnetic action of a voltaic 
current, 202, 381 

on magnetic rotations, 457 
Arc, the electric, theory of, 448 
Arc lamps, 449 

light, 448 
Arc-lighting machines, 468 
Armature of magnet, 103 

of dynamo-electric machine, 
462 
Armstrong, Sir Wm., his Hydro- 
electric Machine, 48 
Astatic magnetic needles, 201 

Galvanometer, 201, 211, 215 
Asynchronous motors, 486 
Atmospheric Electricity, 72, 328 
Atoms, charge of, 491 {footnote) 
Attracted-disk Electrometers, 287 
Attraction and repulsion of elec- 
trified bodies, 2, 4, 22, 24, 
74, 262 



2r 



609 



610 



ELECTRICITY AND MAGNETISM 



The Numbers refer to the Numbered Paragraphs. 



Attraction and repulsion of currents, 
389 

and repulsion of magnets, 84, 
88, 337 

due to influence, 24 
Aurora, the, 153, 159, 161, 336 
Ayrton {W. E.) and Ferry {John) 

ammeter, •221 

on contact electricity, 80 

on dielectric capacity, 293 

secohmmeter, 458 (c) 

value of "v," 359 

voltmeter, 221 
Ayrton and Mather galvanometer, 

216 
Azimuth. Compass, 149, 151 

B. A. UxiT, 353 

Back E.M.F., 445 

Back Stroke, 29 

Bain, Alex., his Chemical "Writing 

Telegraph, 246 
Balance methods. 139, 411, 413 et seq. 

Wheatstone's, 413 
BalUstic Galvanometer, 218, 418 
Bancalari on flames, 3T4 
Barrett, William F., on magnetic 

contraction, 124 
Batteries, voltaic, 16S, 179, 193 
list of, 189 
secondary, 492 
Battery of Levden jars, 62 
Beccaria, Father G., on electric 
distillation, 251 
on atmospheric electricity, 333 
Becqiierel. Antoine Cesar, on atmo- 
spheric electricity, 334 
on dlamagnetism, 369 
Becquerel, Edmond, on photo-vol- 
taic currents, 530 
Becquerel, Henri, on magneto-optic 

rotation, 526 
Bell, Alexander Graham, his Tele- 
phone. 510 
Uses induction balance to de- 
tect bullet, 514 
The Photophone, 529 
Bells, electric, 50S 
Bennet, Abraham, his doubler, 49 

Electroscope, 16, 28 
Best grouping of cells, 192, 407 
Bichromate Battery, ISO, 189 
Bidwell, Shelford', on magnetic con- 
traction, 124 
on susceptibility, 365 
on Mfting power, 384 
Effect of light on magnets, 524 



Bifilar Suspension, 130, 209, 288 

Biot, Jean Baptiste, experiment 
with hemispheres, 33 
Law of magnetic distribution, 

153 
on atmospheric electricity, 334 

Bismuth, diamagnetic properties of, 
94, 370 
change of resistance in mag- 
netic field, 397 

Blasting by electricity, 316, 432 

Blood, conducting power of, 256 

Board of Trade Unit, 440 

Board of Trade Standards, Appen- 
dix B 

Bolometer, 404 

Boltzmann, Lndwig, on Dielectric 
capacity, 297, 298, 518 

Boracite, 74 

Bosanquet, E. H. M., magnetic cir- 
cuit. 375 

" Bound "■ electricity, 27, 79 

Boyle, Hon. Robert, 2 (footnote) 

Boys, Charles Vernon, radio-micro- 
meter, 425 

Brake-wheel arc lamps, 449 

Branched circuit, 409 

Brass, deposition of, 490 

Breaking a magnet, 116 

Breath-figures. 324 

Bridge, Wheatstone's, 418 

British Association Unit, 358 

Broadside-on method, 138 

Brown, C. E. L., on motor, 486 

Brugmans discovers magnetic re- 
pulsion of bismuth, 369 

Brush, Charles F., his dynamo, 468 

Brush discharge, 319, 324 

Brushes, 463 

Bunsen's Battery, 183, 189 

Cable, Atlantic, 301 {footnote), 302, 
323, 504 
submarine, 504 

" as condenser, 301, 

323 
Cabot, Sebastian, on magnetic de- 

chnation, 151 
Cadmium in standard cell, 183 
Cailletet on resistance of air, 313 
Calc-sjtar, 75 

Calibration of Galvanometer, 211 
Callan, induction coil, 229 

Batterv, 183 {footnote) 
Callauds Battery, 187 
Callender's pvrometer, 404 
Calomel cell, 188 



INDEX 



611 



The Xumbers refer to the Numbered Paragraphs. 



Calories and joules, 427, 439 
Candles, electric, 451 
Canton, John, discovers electro- 
static induction, 22 

on electric amalgam, 44 
Capacity, definition of, 271 

in alternate circuit, 473 

measurement of. 418 

of cable. 301 et seq. 

of condenser, oS, 204, 304, 473 

of conductor, 40, 55, 272, 304 

of Leyden jar, 5S, 294 

of liquid condenser, 492 

specific inductive, 25, 56, 295, 
304 

unit of (electrostatic), 272 

unit of (practical), 303 
Capillarj' Electrometer, 253, 292 
Carbon "plates and rods, 183 (foot- 
note) filaments, 452 
Carbons for arc lamps, 449 
Cardew, Philip, his voltmeter, 430, 

471 
Carhart, Henry S., on standard 

ceUs, ISS 
Carnivorous Plants, sensitive to 

electricity, 256 
Carre, F., Dielectric machine, 45 

on magnets of cast metal, 106 
Carriers, 49 
Cars, electric, 446 
Cascade arrangement of jars, 309 
Cautery by electricity, 431 
Cavallo, Tiberius, his attempt to 
telegraph, 497 

his pith-ball electroscope, 4 

on atmospheric electricity, 333 
Cavendish, Hon. H., on Specific In- 
ductive capacity, 295, 296 

on nitric acid produced by 
sparks, 316 
Ceca, Father, on atmospheric elec- 
tricity, 333 
Cell, voltaic, 166 
Cells, classification of, 180 

grouping of, 192, 40T 

fist of, 139 
Centi-ampere balance, 896 
Central stations, 440, 478 
Cu-cuit, 166, 406 

Magnetic, 375 

points of, where energy gained 
and lost, 248, 436 
Circuits, branched, 243, 409 
Circuital magnetism, 118, 347 
Circular current, 345 
City of London central station, 478 



Change of configuration, law of, 204, 

379 
Characteristic curves, 466 
Charge, electric, 8 

resides on surface, 32 
residual of Leyden jar, 61, 299 
of accumulator, 492 
Chart, magnetic, 154 {frontispiece) 
Chemical action, E.M.F. of, 4SS 
Chemical actions in the battery, 172 
laws of, 178, 240, 488 
of spark discharge, 316 
outside the battery, 234, 487 
Chemical test for weak currents, 
246, 316 
depolarization, 180 
Chimes, electric, 46 
Choking-coUs, 474 
Choking eff"ect, 459, 473, 474 
Chromic solution, 183 
Chronograph, electric, 509 
Clamond's thermopiles, 425 
Clark, Latimer, his standard cell, 

188, and Appendix C 
Classification of cells, 180 
Clausius, R., theory of Electrolysis, 

491 
Cleavage, electrification by, 68 
Clock diagram, 470, 472 
Clocks, electric, 509 
Closed circuit, cell for, 176, 181 
Closed-circuit method of Telegraphy, 

500 
Closed-coil armature, 463 
Cobalt, magnetism of, 93 
CoeflScient of Magnetic induction 
(see Permeability) 
of Magnetization (see Sus- 
ceptibility) 
of mutual-induction (or poten- 
tial), 351, 454 
of self-induction, 458 
Coercive force, 96, 367 
Colour of spark, 318 
Columbus, Cristofero, on magnetic 

variation, 151 
Combs on influence machine, 42, 50 
Combustion a source of electrifica- 
tion, 70 
heat of, 488 
Commercial efficiency of dynamo, 

464 
Commutator, 443, 461, 463 
Compass (magnetic), Mariner's, 87, 
149 
error due to iron ship, 149 
Compound circuit, 192, 243, 409 



612 



ELECTRICITY AND MAGNETISM 



The Numbers refer to the Numbered Paragraphs. 



Compound dynamo, 465, 467 

magnets, 104 
Condensation, 56 
Condenser, 56, 294, 303 

capacity of, how measured, 
418 

discharge of, 326, 515 

in alternate circuit, 473, 474 

liquid, 492 

method of measuring a resist- 
ance, 411, 417 

standard, 303 

use of, 229, 302 
Condensing electroscope, 79 
Conductance, 402, 404 
Conduction, 7, 30, 171, 402, 404, 476 

by liquids, 234, 404 

of gases, 171, 322 
Conductivity, 171, 322, 846, 348, 402, 

404 
Conductor cutting lines, 225, 339, 

353, 355 
Conductors and Non-conductors, 8, 

27, 30, 402 et seq. 
Conductors electrified by rubbing, 13 

opaque, 518 
Consequent Poles, 117, 120, 382 
Constant-current dynamos, 468 

voltage dynamos, 467 
Contact Electricity, 79, 163 

Series of metals, 80 

rings, 461 

of surfaces, 12 
Continuous-alternate transformers, 
483 

currents, 162 

current dynamos, 463 

current transformers, 482 

electrophorus, 26, 49 
Contraction due to magnetism, 124 
Control of galvanometer, 209 
Convective discharge, 312 
Convexion of electricity, 49, 812, 897 

currents, 397 

induction machines (see In- 
fluence machines) 

streams at points, 88, 47, 274, 
329 
Cooking by electricity, 484 
Coohng and heating of junction by 

current. 419 
"Corkscrew Eule," 198 
Cost of power derived from elec- 
tricity, 440 
Coulomb, Torsion Balance, 18, 132 

Law of Inverse Squares, 19, 
129, 132, 261, 270 



Coulomb on distribution of charge, 

38, 273 
Coulomb, the, 162, 354 

how manv electrostatic units, 
262 (footnote) 
Couple, magnetic, 136 
Couphng of alternators, 479 
Creeping, stopped by parafiin, 183 

magnetic, 368 
CrooJces, William, on shadows in 
electric discharge, 321 
on repulsion from negative 
electrode, 327 
Crown of cups, 165 
Cruickshank's Trough Battery, 180 
Crystallization, 69 
Crystals, electricity of, 74, 75 

dielectric properties of, 297 
magnetism of, 373 
Gumming, James, invents galvan- 
ometer, 200 
thermo-electric inversion, 423 
Cuneus' discovery of Leyden jar, 60 
Curbing telegraphic signals, 302 
Current, effects due to, 167 
Electricity, 162 
strength of, 171, 190 

unit of, 162, 207 
Current, is the magnetic whirl, 202 
balance, 396, and Appendix B 
sheets, 410 
Currents, very large, measurement 

of, 412 
Curvature affects surface-density, 

38, 274 
Curve-tracer, 368 
Curves, magnetic (see Magnetic 

Figures) 
Curves of magnetization, 364 

characteristic of dynamos, 466 
Cuthbertson, John, his electric 

machine, 41 
Cycles of magnetization, 868 

of alternate currents, 470 
Cylinder Electrical machine, 42 

Daily variations of compass, 156 
Dalibard's lightning-rod, 329 
Damping galvanometers, 219 
Daniell, John F., his cell, 181, 184 
D'Arsonval. galvanometers, 216 
Davy's (Marie) Battery, 193 
Davy, Sir Humphry, magnetiza- 
tion by current, 381 
discovers electric hght, 448 
electrolyses caustic alkalies, 
490 (c) 



INDEX 



613 



The Numbers refer to the Numbered Paragraphs. 



De Haldat. magnetic writingr, 122 
De la Rive's Ffoating Battery, 205 
De la Rue. Chloride of Silvei- Batterv, 
1>G. 313 

on electrotyping, 495 

on length of spark, 313 
Dead-beat galvanometers, 219 
Declination, Magnetic, 151 

variations of, 151, 155 
Decomposition of water, 235 

of alkalies, 490 (o) 
De-electritication bv flame. 314 
Deflexions, method of, 131, 136 
Deflexion of galvanometer, 210 
Dellmann' s electrometer, 286 
Demasi-netize, how to, 363 
Density (surface) of charge, 38, 273, 

magnetic, 134, 337 
Depolarization, mechanical, ISO 

chemical, ISO, 1S2, 1S3 

electro-chemical, 180, 181 
Deposition of metals, 494 
Deviation of compass, 149 
Dewar. James, on currents gen- 
erated by hght in the eye, 
257 

his capillary electrometer, 253 

mag-netic properties of iron at 
200°, 111 

oxygen, magnetic, 370 
Dewar and Fleming, resistance at 

low temperattire, 404 
Diagram, thermo-electric, 424 
Dial bridge, 415 
Diamagnetic polarity, 369 
Diamagnetism, 94, 369 

of flames, 374 

of gases, 370, 374 
Diaphragm currents, 254 
Dielectric capacity, 295 to 299 

capacity, effect on intensity of 
field,' 262, 298 

coelficient, 283, 517 

strength, 315 
Dielectrics, 10, 25, 57, 295 
Difference of potential, 265 

magnetic potential, 337 
Differential galvanometer, 217, 411 
Dimensions of units, 356 
Di-phase currents, 485 
Dip, or Inclination, 152 

variation of, 155 
Diplex signalling, 503 
Dipping Needle, 152 
"Direct" and "inverse" current, 

223 
Direction of induced E.M.F., 226.450 



Discharge affected by magnet, 322 

brush, 319, 324 

by evaporation, 251 

by flame, 8, 314 

by points, 47, 319, 329 

by water dropping, 334 

conductive, 310 

convective, 47, 312 

disruptive, 311 

effects of, 47, 315, 316, 317 

glow, 319, 329 {footnote) 

limit of, 273 

oscillatory, 515 

sensitive state of, 322 

striated, 320 

through gas at low voltage, 
322 

velocity of, 323 
Discharger, Discharging-tongs, 59 

Universal, 62 
I Disk armature, 463 
' Displacement, electric, 57 
I currents, 516 

I Disruption, electrification by, 68 
Dissectible Leyden jar, 63 
Dissipation of Charge, 326 
Dissociated gases conduct, 322 
Distillation, electric, 251 
Distribution of Electricity, 31 to 38, 
273, 274 

of Magnetism, 117, 134 
Distribution by transformers, 480 
Distribution of energy, 440 
Distortion of dynamo-field, 463 
Divided circuits, 409 

Touch, 101 
Dolbear, A. E., his telephone, 299, 

510 
Doubler, the, 26, 49 
Double refraction by electric stress, 

524, 525 
Double Touch, 102 
Dreh-strom, 485 

Drop of voltage in mains, 412, 447 
Dry cells, 184, 189, 193 
Dry-Pile, 193, 291 
Du Bois, limit of magnetization, 363 

measurement of permeability, 
366 
Duboscq, Jules, his lamp, 449 
Du Fay's experiments, 5, 30 
Duplex Telegraphy, 302, 503 
Duration of Spark, 323 
Dust, allaying, 54 
Duter on Electric Expansion, 300 
Dynamic Electricity (see Current 
Electricity) 



614 



ELECTRICITY AND MAGNETISM 



The Numbers refer to the Numbered Paragraphs. 



Dynamos, 461 

as motors, 443, 463 
Dynamometer, 394 
Dyne, the (unit of force), 281 

Eakth, the, a magnet, 95 

cm-rents, 302 

electrostatic capacity of, 303 

intensity of magnetization, 365 

magnetic force in absolute 
units, 361 

used as return %vire, 497 
Earth's magnetism (see Terrestrial 

Magnetism) 
Earth, potential, 269 
Eheri, H., on oscillations, 522 
Eddy-currents. 457, 477. 486 
Edison, Thomas Alva, electric 
lamp, 452 

carbon telephone, 511 

meter for currents, 244, 442 

quadruplex telegi-aphy, 503 
Edlund on galvanic expansion, 249 
Eel, electric (Gymnotus), 76 
Efficiency of transmission, 447 

of "dj-namos, 464 

of motors, 445 

of transformers, 481 
Electric Ak-Thermometer, 317 

Cage, 37 

Candle, 451 

Clocks, 509 

Displacement, 57 

DistUlation, 251 

Egg, the, 232, 320 

Expansion, 300 

Field, 13, 16, 20, 22, 24, 262, 
279, 299. 524. 525 

Force, 169 (footnote), 266 

(Frictional) machines, 42 

Fuze, 316, 429, 432 

Images, 275 

Kite. 329 

Light, 448 

Lines of Force, 13, 16, 20, 22, 
24, 299 

Mill or Fly, 47 

Oscillations, 515 

Osmose, 250 

Pistol, 316 

Shadows, 321 

Shock, 254 

Stress, 13, 16, 20, 22, 24, 63, 
279 

Waves, 515 

Wind, 47, 324 
Electrics, 2 



Electricity, theories of, 7, 327 

word fii'st used, 2 (footnote) 
Electro-capillary phenomena, 253 
Electro-chemical Depolarization, 180 

equivalents, 240, 489 

power of metals, 489 
Electro-chemistry, 487 

deposition,' 494 
Electrodes, 236 

unpolarizable, 257 
Electrodynamics, 389 
Electrodynamometer, 394 
Electrolysis, 237, 487 

in discharge. 322 

laws of, 240, 490 

of copper sulphate, 238 

of water, 236, 487 

theorv of, 491 
Electrolytes, 236, 487 
Electrolytic condenser, 492 

convexion, 491 
Electi-omagnet, alternate current, 

477 
Electromagnets. 107, 381 

laws of, 380 

calculations for, 375, 376 (and 
see p. 595) 
Electromagnetic engines (see Mo- 
tors) 
Electromagnetic svstems, law of, 
204, 379 

svstem of units, 352 

theory of Light, 517 

waves, 515 
Electromagnetics, 337 
Electromagnetism, 337 
Electrometallurgy', 494 
Electrc^meter. absolute, 287 

attracted-disk, 287 

capillary. 253. 292 

Bellmdnn's. 286 

Peltier's, 2^6, 3a' 

portable. 2S7 

quadrant {Lord Kelvin's), 288 

i-epulsion, 286 

torsion. IS 

trap-door, 287 
Electromotive-force, 169, 487 

induced, 222 

measurement of, 416 

unit of, 354 
Electromotive intensity, 266, 283 
Electromotors, 443, 484 
Electro-Optics, 524 
Electrophorus, 26 

continuous, 26, 49 
Electroplating, 496 



INDEX 



615 



The Xumhers refer to the Numbered Paragraphs 



Electroplating, dynamos for, 462 
Electroscopes, 14 

Bennet's ?old-leaf, 16, 28 

Bohnenberger's, 16, 291 

Fechner's. -291 

Gilbert's straw-needle, 15 

Bankers, 291 

Henley's quadrant, 17 

Pith-ball, 3, 4 

Volta's condensing, T9 
Electroscopic powders, 31, 4T, 299, 

324 
Electrostatic Optical Stress, 525 

voltmeter, 290 
Electrostatics, S, 259 
Electrotyping, 495 
Element of Current, 344 
Elwell- Parker alternator, 478 
End-on method, 138 
Energy, 1, 64 

of magnetic field, 202 

of charge of Leyden jar, 305 

of electric current, 435 

paths, 513 

points in circuit where it is 
lost or gained, 248, 436 

supply and measurement of, 
435 
Equator, Magnetic, 86 
Equipotential surfaces, 267 

magnetic, 337 (f) 
Equivalents, electro-chemical, 240 
Erg. the (unit of work), 281 
Ether, 1, 7, 64, 517 
Evaporation produces electrification, 
71, 330 

discharge by, 251 
Everett, James Z)., on atmospheric 
electricity, 334 

on exact reading of galvan- 
ometer, 214 {footnote) 

on intensity of magnetization 
of earth, 365 
Ewing, James A., on limit of mag- 
netization, 363 

curves of magnetization, 364 

theory of magnetism, 127 
Exchanges, telephone, 513 
Excitation of Field-magnets, 465 
Exciting power, 377 
Expansion, electric, 300, 525 
Extra-current, 459 

Faiitjee and exhaustion of bat- 
teries, 172 

FaU of potential along a wire, 289, 
412 



Farad, the (unit of capacity), 303, 354 
Faraday. Afichael, molecular theory 
of electricity, 7 
chemical theory of cell, 178 
dark discharge, 319 
diamagnetism, 369, 373, 374 
discovered inductive capacity, 

25, 296, 298 
discovery of magneto-induc- 
tion, 222 
Disk machine, 227 
electromagnetic rotation, 393 
experiment on dielectric po- 
larization, 299 
gauze-bag experiment, 34 
hollow-cube experiment, 34 
ice-pail experiment, 37 
laws of electrolysis, 240, 242 
length of spark, 313 
Magnetic lines-of-force, 119 
magnetism in crystals, 373 
on Arago's rotations, 457 
on dissipation of charge, 314 
on electrodynamics, 392 
on identity of different kinds 

of electricity, 245, 246, 316 
predicted retardation in ca- 
bles, 301 
Eing, 228 
rotation of plane of polarized 

hght, 526 
voltameter, 242 
Faure, Camille, his Secondary Bat- 
tery, 492 
Favre's experiments on heat of 

currents, 428 
Fechner''s electroscope, 291 
Feddersen, W., on electric oscilla- 
tions, 514 
Feeders, 440 

Ferromagnetic substances, 369 
Field, electric, 13, 16, 20, 22, 24, 262, 
279 299 525 
magnetic, 115, 202, 337, 462, 526 
Field-magnet, 462 
Field-magnets, excitation of, 465 
Field-plate, 50 

Figures, magnetic (see Magnetic 
Figures) 
electric, 31, 299, 324 
Filament of incandescent lamps, 452 
Filings for mapping fields, 121 
Fire of St. Elmo, 329 (footnote) 
Flame, currents of, 314 

diamagnetism of, 374 
discharge by, 8, 814 
produces electrification, 70 



616 



ELECTRICITY AND MAGNETISM 



The Numbers refer to the Numbered Paragraphs. 



"Flashing" filaments, 452 
Fleming and Dewar, resistance at 

low temperature, 404 
Fleming, John Ambrose, his Bat- 
tery, 193 
rule as to direction of E.M.F., 
226 
Flux, magnetic, 142, 337, 363, 377 

density, 363 (footnote) 
Fontana on electric expansion, 300 
Force, electric. 169 {footnote), 266, 
276, 277 
electromotive (see Electromo- 
tive force) 
magnetic, 91, 169 {footnote), 

337 
near a straight conductor, 207, 

348 
on conductor in field, 340, 341 
Form, effect of, on retenti\-ity, 98 

on lifting power, 114 
"Forming" accumulator plates, 492 
Foster, George Carey, his evalua- 
tion of ohm, 358 
method of testing, 415 
Foucault, Leon, his Regulator 
Lamp, 449 
Interruptor, 229 
Foucault-currents (see Eddy-cur- 
rents) 
Franklin. Benjamin, discovered ac- 
tion of points, mentioned in, 
38 (C), 47, 329 
cascade arrangement of Ley- 
den jars. 309 
Electric chimes, 47 
Electric kite, 329 
Electric portraits, 317 
his charged pane of glass, 55 
invents lightning conductors, 

329, 332 
kills turkey by electric shock, 

254 
One-fluid theory of electri- 
city, 7 
on seat of charge, 63 
theory of the aurora, 336 
Frankfort, "transmission of power 

to, 447, 485 {footnote) 
" Free " electricity, 27, 79 {footnote) 
Frequency, 470, 476 

of oscillations, 515, 520 
Friction produces electrification, 2, 12 
Frog's legs, contractions of, 163, 255 
Frolich, Otto, on electromagnet, 380 
Froment's motor, 443 
Fuel, zinc as, 166 



Fuses, 316, 429, 432 
Fusing of wires, 429 



" G" of galvanometer, 213 
Galvani, Aloysius, observed move- 
ments of frog's leg, 163 
on preparation of frog's limbs, 

255 
on Animal Electricity, 257 
Galvanic Batteries (see Voltaic Bat- 
teries) 
Electricity (see Current Elec- 
tricity) 
Taste, 254 
Galvanism (see Current Electri- 
city) 
Galvanometer, 208 
absolute, 213 
astatic, 211, 215 
ballistic, 218, 418 
constant of, 213 
damping of, 219 
D'ArsonvaVs, 216 
dead beat, 219 
difi^erential, 217, 411 
Du Bois Beymond's, 257 
reflecting {Lord Kelvin's), or 

mirror, 215 
sine, 214 
tangent, 212 

Von Helmholtz's, 212 {foot- 
note) 
Galvanoplastic (see Electrotyping) 
Galvanoscope, 199 
Gas Battery, 493 
Gases, dissociated, conduct, 822 
resistance of, 171, 314, 322 
Gassiot, J. P., on striae, 322, 827 
Gaugain, Jean Mothee, 

on P}Toelectricity, 74 
Tangent Galvanometer, 212 
(footnote) 
Gauss, C. F., invented absolute 
measurement, 352 
magnetic force of the earth, 

361 
magnetic observations, 365 
on magnetic shell, 348 
Gay-Lussac, on atmospheric elec- 
tricity, 334 
Geissler's tubes, 320 
Generators of alternate currents, 473 

continuous currents, 463 
Gernez on electric distillation, 251 
Gibson and Barclay on dielectric 
capacity of parafiin, 297 



INDEX 



617 



The Numbers refer to the Numbered Paragraphs. 



Gilbert, Dr. William, discovers 
electrics, 2 
discovered magnetic reaction, 

91 
discovers that the earth is a 

magnet, 95, 150 
heat destroys magnetism, 

109 
his balanced - needle electro- 
scope, 15 
his terreUa, 95 
observation of moisture, 10 
observations on magnets, 86 
on de-electrifving power of 

flame, 314 
on magnetic ligures, 119 
on magnetic substances, 92 
on magnetic permeability, 97 
on methods of magnetization, 
105, 106 
Glass, a conductor when hot, 31 
Globular lightning, 831 
Glow Discharge, 319, 329 {footnote) 

lamps, 452 
Gold-leaf Electroscope (see Electro- 
scope) 
Gordon, J. E. H., on magneto-optic 
rotatorv power, 526 
on dielectric capacity, 29T, 

293 
on length of spark, 813 
Gramme, Zenohe Theophile, his 

ring-armature, 463 
Gravity Battery, 1S7 
Gray, Andrew, Absolute Measure- 
ments in E. and ^Si., 136 
(footnote). 2ST (footnote), 
396 (footnote) 
Gray, Stephen, discovers conduc- 
tion, 30 
on lightning, 329 
Grid of accumulator, 492 
Grotthuss' theory, 172, 491 
Grouping of arc lamps, 450 
cells, 192, 407 
glow-lamps, 453 
CrTOve, Sir William R., his Gas 
Battery, 493 
Grove's Battery, 182 
magnetic experiment, 124 
on electric property of flame, 
314 
Guard-ring, Guard-plate, 273, 287 
GhiericJce, Otto von, discovered 
electric repulsion, 4 
invents electric machine, 41 
observes electric sparks, 11 



Gunpowder fired by electricity, 316, 

317, 432 
Guthrie, Frederick, effect of heat 

on discharge, 314 
heating of kathode in water, 

483 
Gymnotus (electric eel), 76, 246 

Half deflexion method, 417 
Hall, Edward H., his effect, 897 
Hankel, Wilhelm G., his electro- 
scope, 291 
Hardening of steel, 108 
Harris, Sir W. Snow, his unit 
Leyden jar, 285 
attracted - disk electrometer, 

■287 
on length of spark, 313 
Haukshee, Francis, on thunder- 
storms, 329 
Haiiy, The Abbe, his astatic method, 

201 
Heat and resistance, 426, 439 
of combination, 488 
effect of, on magnets, 109, 111 
" batteries, 194 

" GeissZer tube, 320 

" resistance, 404 

emission, 386, 429 
Heat, unequal action of, on -I- and — 

charges, 814, 327 
Heating of coils, 386, 429 
Heating effects of currents, 182, 426, 
439 
due to magnetization, 124, 368 
effect of sparks, 317 

" dielectric stress, 299 
local, at electrodes, 491 
Heaviside, Oliver, reluctance, 875 
(footnote) 
on energy paths, 518 
on quadruplex telegraphy, 497 
Helmholtz, Hermann L. F. von, on 
effect of current on sight, 
254 
Electrolytic convexion, 491 
Equations of self-induction, 

460 
Galvanometer, 212 (footnote) 
Hemihedry in crystals, 75 
Henry, Joseph, invented the " soun- 
der," 497 
on induced currents of higher 
orders, 455 
Henry, the, 854, 454, 458 
Hertz, Heinrich, on effect of ultra- 
violet waves, 318, 531 



618 



ELECTRICITY AND MAGNETISM 



The Numbers refer to the Numbered Paragraphi 



Hertz, Heinrich, kathode rays, 321 
researches on electric waves, 
5-20 
Heydweiller, on length of spark, 313 
Hittorf, on discharge, 322 
Hiah frequency, 476, 515, 520 
Holtz, W., his electric machine, 53 
on electric shadows, 321 
on tubes having unilateral 
resistance, 327 
HopMnson, John, on dielectric ca- 
pacity of glass, 297 
on residual charge and its 

return, 299 
on magnetization, 364 
his characteristic curves, 466 
Horizontal component of magnetism, 

136, 158, 361 
Horse-power and watts, 435 
Hot glass, a conductor. 31 
Hughes f David Edward, the Print- 
ing Telegraph, 4ii7 
the Microphone, 512 
magnetic balance, 140 
induction balance, 514 
Humboldt, Alexayider von, on elec- 
tric eels, 76 
discovers galvanic smeU, 254 
produced electric contractions 
in fishes, 255 
Hunter, Dr. John, on effect of cur- 
rent on sight, 254 
Hydi'oelectric machine, 4S 
Hysteresis, 367, 368 



Idiostatic method of using volt- 
meter, 290 
Images, electric, 275 
Impedance, 472 
(Impedance) coUs, 474 
Incandescent lamps, 452 
Inclination (or Dip), 152 

variation of, 155 
Index Xotation, 355 
Inductance, 453 
Induced charges of electricity, 22 

currents. 222 
Induction (electrostatic) of charges, 
(see Influence) 
{magnetic) hues of, 96 
(magnetic) of magnetism, 96 
(magneto-electric) of cur- 
rents, 222 
(volta-electric) of currents by 
currents (see Self induc- 
tion. Mutual induction) 



Induction, the, meaning the internal 
magnetization, 363 (foot- 
note) 

Induction-coU or Inductorium, 229 

Induction-convexion machines, 49 

Inductive-capacitv, specific, 25, 56, 
295, 299 

Inertia, electromagnetic, 453 

Influence, 22 

Influence-machine, 49-54 

Insulators. 10. 30. 405 

Intensity of current, 190 (footnote) 
of earth's magnetic force, 153, 

35S, 361 
of magnetic field, 338 
of magnetization, 365 

Internal resistance, 171, 406, 417 
of armatures, 462 

International ohm, 358 

'"Inverse"' and "direct" cuxrents, 
223 

Inverse Squares, Law of, 19, 129, 
14S, 261, 270 

Inversion, Thermo-electric, 423 

Ions, 239 

Ironclad magnet, 383 

Iron, properties of, 362 

Iron rods red hot in water, 433 

Isochnic hues, 154 

Isogonic lines, 154 

Isolated, 271 



Jablochkoff, Paul, his battery, 
iy3 
electric candle. 451 
Jacohi, Moritz Hermann, on local 
action, 174 
discovers galvanoplastic pro- 
cess, 495 
his boat propelled by electri- 
city, 443 
on electromagnet, 380 
theory of electromotors, 443 
Jar, Levden, 59 

capacity of, 58, 294, 304 
" cascade arrangement 

of, 309 
" discharge of, 59, 310, 

515 
" discovery of, 60 
" energy of charge of, 

305 
" seat of charge of, 63 

spark of, 318, 323 
" theorv of, 294 
Unit, 285 



INDEX 



619 



The Numbers refer to the Numbered Paragraphs. 



Jenkin, Fleeming, on cable as con- 
denser, 301 
on retardation in cables, 323 
Joints in magnetic circuit, 3T8 
Joule, James Prescott, on effects of 
magnetization, 124 
evaluation of ohm, 353 
Law of heat of current, 427, 

439 
limit of magnetization, 363 
magnetic circuit, 3T5 
Mechanical equivalent of heat, 

439, 4SS 
on atmospheric electricity', 

333 
on lifting-power of electro- 
magnet, 384 
Joule effect, 420 
Joule, the, 354, 439 

Kapp, Gisbebt, on magnetic circuit, 

377 
Kathode, 170, 236 
Kathodic "rays," 321 
Kation, 239, 491 
Keeper, 103 

Kelvin, Lord (Sir William Thom- 
son) 
Attracted-disk Electrometer, 

79, 287 
Compass, 149 
Current Balances, 396 
Divided ring Electrometer, 79 
Electric convexion of heat 

(Thomson effect), 424 
Evaluation of ohm, 358^ 

Modified Daniell's cell, 187 
on atmospheric electricity, 333 
on electric images, 275 
on electi-ostatics, 287 {foot- 
note) 
on length of spark, 313 
on nomenclature of magnetic 

poles, 89 {footnote) 
on sounds in condensers, 299 
predicts electric oscillations, 

515 
proof of contact electricity, 

79 
Quadrant Electrometer, 288 
Eeplenisher (or Mouse MUl), 

49, 287, 288 
Thermo-electric diagram, 424 
Water-dropping Collector, 834 
Kerr, Dr. John, Electro-optic dis- 
coveries, 300, 525 



Kerr, Dr. John, Magneto-optic dis- 
coveries, 125, 366, 527 

Kerr's effect, 5-27 

Kinnersley, Elijah, Electric Ther- 
mometer, 317 

Kirchhoff, Gustav, Laws of 
Branched Cii-cuits, 409 

Kite, the electric, 329 

Kohlrausch, Friederich, on resid- 
ual charge, 299 
on electro-chemical equivalent, 

240 
on evaluation of ohm, 358 

Ku7idt, August, his effect, 528 



Lag and lead, 472 

Lagging of magnetization, 368 

Lamellar magnetization, 118 

Laminated magnets, 104 

Lamination of cores, 457, 463, 477, 480 

Lamps, arc, 449 

Lamps, incandescent, 452 

Langley, S. P., his bolometer, 404 

Law, cell, 180 

Laws of electrolysis, 490 

of inverse squares, 19, 129, 
148, 261, 270 

of electro-magnetic system, 
204, 379 
Lead, used in accumulators, 492 

no Thomson-effect in, 424 
Lead and lag, in phase, 472 
Lead of brushes, 463 
Leakage, magnetic, 377 

photoelectric, 531 

rate of electric, 326 
Le Bailliff, diamagnetism, 369 
Leclanche, Georges, his cell, 184 
Lemonnier discovers atmospheric 

electricity, 333 
Lenard, Philipp, aluminium "win- 
dow," 321 
Length of spark, 313 
Lenz's Law, 456 
Lenz on electromagnet, 380 
Leyden jar, 55 

prevention of piercing spark, 
62 

oscillatory dischai-ge of, 515 

resonance between two, 517 

seat of charge in, 63 
Leyden s (see Condensers) 
Lichtenberg' s figures, 324 
Life of Lamps, 452 
Lifting-power of magnets, 113, 114 

of electromagnets, 384 



620 



ELECTRICITY AND MAGNETISM 



The Numbers refer to the Numbered Paragraphs. 



Light affects resistance, 529 
affects a magnet, 524 
Electric, 4SS 
Electromagnetic theory of, 1, 

518 
polarized, rotated by magnet, 

125, 526, 527, 528 
velocity of, 359, 518 
Lightning, 11, 329, 331 
Lightning conductors, 35, 332 
duration of, 323, 331 
best methods of protection 
from, 332 
Limit of heating of electromagnet, 
386 
magnetization, 363 
Lines-of-force, electric, 13, 16, 20, 22, 
24, 268 
magnetic, 96, 119, 33T 
Line-integral, 341 (footnote) 
Lippmann, G., Capillary Electro- 
meter, 253, 292 
Liquids as conductors, 234, 490, 518 

resistance of, 403, 404 
Liquid condensers, 492 
" Local Action " in batteries, ITS 
Locomotion, electric, 446 
Lodestone. 84 

Lodge, Oliver, on resonance, 517 
his oscillator, 521 
his detector or coherer, 521 
London, city of, Central Station, 

478 
" Long " and " short " coils for mag- 
nets, 386 
Long and short coU instruments, 

408 
Lorenz. L., on evaluation of ohm, 

358 
Loss of charge, 326, 531 
Louis XV. electrifies 700 monks, 254 
Lullin's experiment, 315 
Luminous effects of spark, 318 

Machine, Electric, 42 

alternate-current, 478 

cylinder, 42 

dvnamo-electric, 461 

Holtz's, 53 

hydro-electrical, 48 

influence, 49 

magneto-electric, 461 

plate, 43 

Toepler's or Voss, 51 

Wimshurst. 52 

Winter s, 43 
Magne-crystallic action, 373 



Magnet, breaking a, 116 

Magnets, natural and artificial, 84, 

85 
Magnetic actions of current, 195, 

338, 389 
attraction and repulsion, 88, 

121, 389 
cage, 97 
creeping, 368 
Magnetic circuit, 375 

field, 115, 202, 389 

** rotatory, 485, 486 
figures, 119. 120, 121, 202, 389 

theory of, 142 
flux, 337, 377 

flux density, 363 (footnote) 
force, 91, 337 (a) 

" measurement of, 130 
hysteresis. 367, 368. 464 
induction, 96, 363 {footnote) 
iron-ore, 84 
lae-, alleged, 368 
lines-of-force, 96, 119, 120, 121, 

349, 362, 373, 377, 389, 464 
lines-of-force of current, 202, 

389 
maps, 154 
meridian. 151 
metals, 93. 362, 869 
model (Ewing's), 127 
moment. 135, 346, 361 
needle, 87, 149 

oxide of kon, 84, 183 {foot- 
note) 
paradox, a, 143 
permeabihty, 96, 363, 366, 518 
pole, unit, 141, 352 
potential, 337, 347, 348 
proof-plane, 232 
saturation, 112. 363 

JSeetz, on, 126 
screen, 97 
sheU, 118, 203,337 (fe), 348 

" force due to, 345 

" potential due to, 348 
storms, 158, 336 
substances, 92, 362, 369 
susceptibihty, 365 
units, 352 
writing, 122 
Magnetism, 84 

action of, on light, 125, 126 

destruction of, 109 

distribution of, 117 

lamellar, 118 

laws of, 89, 128, 337 

of gases, 370, 374 



INDEX 



621 



The Xumhers refer to the Numbered Paragraphs. 



Magnetism, permanent, 93 

phenomenon of rotation, 526 

residual, 112, 364 

solenoidal, llS, 347 

temporary, 9S, 112 

terrestrial, 95, 150 

theories of, 99, 126, 526 

unit of, 141, 352 
Magnetite, 84 
Magnetization, anomalous, 3T3 

coefficient of (see Suscepti- 
bility) 

cycles of, 361, 363 

intensity of, 365 

lamellar, 113 

mechanical effects of, 124 

methods of, 100-107 

solenoidal. 118, 347 

sound of, 124, 510 

time needed for, 333 
Magneto-electricity, 82, 222, 461 
Magneto-electric machines, 461 
Magnetographs, 160 
Magnetometer, 137 

self-registering, 160 
Magnetomotive-force, 341, 375 
Magneto-optic Eotations, 524 
Magnets, see also electromagnet 

action of light on, 524 

artificial, 85 

compound, 104 

forms of, 103 

lamellar, 113 

laminated, 104, 477 

methods of making, 100-107 

natural, 84, 103 

power of, 114 

unvarying, 110 
Mance, Sir Henry, his method, 417 
Manganese steel, 363 
Manganin, 404 
Maps, magnetic, 154 
Mariner's Compass, 149 
Marked pole, 88 

Marum heating by discharge, 317 
Mascart, E., on atmospheric elec- 
tricity, 335 
Matteucci, Carlo, on physiological 
effects, 76, 256 

on electromotive - force in 
muscle, 257 
Maynooth Battery (see Gallants 

Battery) 
Maxwell, James Clerk, Electro- 
magnetic theory of light, 
397, 513 

Law of alternate currents, 473 



Maxioell, James Clerk, Law of 

electromagnetic system, 204, 
349, 379 
measurement of " w," 359 
on Electric Images, 275 
on protection from lightning, 

35, 332 
on residual charge of jar, 299 
rule for action of current on 

magnet, 204, 349 
Theorem of equivalent Mag- 
netic shell, 203, 351 
Theory of Magnetism, 126 

Measureioent of capacity, 418 
of currents, 221, 395, 412 
of E.M.F., 416 
of internal resistance, 417 
of magnetic forces, 130 
of mutual induction, 454 
of permeability, 366 
of power, 437 
of resistance, 411, 412 
of self-induction, 458 

Mechanical depolarization, 180 

effects of discharge, 47, 315 
" of magnetization, 124 
" in dielectric, 299, 525 

Medical Applications of Electricity, 
258 

Medium, action in, 5, 13, 279 

elasticity and density of, 360 
energy paths in, 519 
velocity of waves, in, 359, 518 

Mega-, 354 

Megohm, 354 

Meidinger's Battery, 187 

Melloni, Macedonio, his thermo- 
])ile, 425 

Mendenhall, T. C, U. S. Geodetic 
Survey, 155 

Meridian, Magnetic, 151 

Metallo-chromy, 490 

Metals, electro-chemical power of, 
489 
electro-deposition of, 494 
refining by electricity, 494 
specific resistance of, 403 

Meter Bridge, 415 

Meters, 442 

Metric system, the, 280 

Mho, the, 402 

Mica, dielectric capacity of, 296 

Micro-, 354 

Microfarad, the, 283, 354 
condenser, 303 

Microphone, the, 512 

Milli-, 354 



622 



ELECTRICITY AND MAGNETISM 



The Numbers refer to the Numbered Paragraphs. 



Milli-ampere, 354 

Mimosa, tne electric behaviour of, 256 

Minotto's cell, 187 

Mirror Galvanometer, 215 

Molecular action of magnetism, 126 

actions of current, 249 

theory of Electric action, 7 
Moment of Couple, 136 
Moment of circular coil, 346 

of inertia, 361 

magnetic, 135, 361 
Morse, Samuel F. B., his Telegraph 

instrument, 499 
Morse Alphabets, the, 499a 
Mordey's alternator, 478 
Motion, law of, in magnetic field, 

204, 379 
Motor-dynamos, 482 
Motors, 443 

alternate-current, 484 
Moulton, John Fletcher, on sensi- 
tive state. 3-22 
Mouse-mill (see Replenisher) 
Muller, Johannes, on strength of 

electromagnets, 380 
Multicellular voltmeter, 290 
Multiplier, Schweigger's, 200 
Muscular contractions, 255, 257 
Mtisschenbroek, Peter van, dis- 
cover}' of Leyden jar, 60 

on Magnetic Figures, 121 
Mutual induction, 454 

potential, 351 

Napoleon III.'s cell, 193 
Navigation, electric, 443 
Needle, magnetic, 87 
telegraph, 498 
Negative electrification, 5, 827 
Network mains, 440 
Neutralizing brush, 50 
Newton, Sir Isaac, observations 
on action and reaction, 91 
his lodestone, 114 
suggests electric origin of 

lightning, 11, 329 
suggests glass for electric 
machines, 41 
Niagara Falls, transmission of power 

from, 447 
Niaudet, Alfred, his cell, 184 
Nickel, 93, 364 

Nobili, Leopoldo, on muscular con- 
tractions, 76 
on currents of animal elec- 
tricity, 257 
discovers Nobili's rings, 490 



Non-conductors, 10, 405 

Non-electi-ics, 3 

North and south, 89, 150 

magnetic pole, the, 89, 150 
Null methods. 210, 289, 411 (c), 413, 
416 (6), 417 {e),418{d) 

Oblique currents, laws of, 390 
Oersted, Hans Christian, discovers 

magnetic action of current, 

195, 196, 202 
Ohm, Dr. Georg Simon, 190 
"Ohm's Law," 191, 399 
Ohm, the, 354, and Appendix B 

evaluation of, 358 
Oil, dielectric strength of, 315 
One-fluid theory of electricity, 7 
Opposition method, 417 
Optical strain, electrostatic, 525 

rotation, electromagnetic, 526, 

527, 528 
Oscillations, electric, 332, 515 

method of (in galvanometry), 

210 
method of (for electrostatics), 

133 {footnote) 
method of '(for magnetic mea- 
surement), 133, 134, 361 
Oscillator, 520, 522 
Osmose, electric, 250 
Other sources of electrification than 

friction, 12, 65 
Output of dynamo, 464 
Over-compounding, 467 
Overhead line for tramcars, 446 
Oxygen, magnetic, 370 
Ozone, 237, 316, 329 {footnote) 

PAClNOTTrs armature, 463 
Page, Charles G., discovers mag- 
netic sounds, 124 
Parallel, capacities in, 307 

cells in, 168, 406 

circuits, laws of, 390 

lamps in, 453 

resistances in, 409 

running of alternators, 479 
Paramagnetic bodies, 369 
" Passive " state of iron, 183 
Pathological dose of current, 258 
Peace, on length of spark, 313 
Peclet, electrification by rubbing, 73 
Peltier, Athanase, his electrometer, 
286, 334 

heating eft'ect at junctions, 420 

theory of thunderstorms, 330 



INDEX 



623 



The Numbers refer to the Numbered Paragraphs. 



Peltier effect, 420 

Penetrative power of discharge, 815 
Periodic current, 470 
Periodicity (see Frequency) of 
aurora and magnetic storms, 
15S, 159, 336 
Permeability, 96, 363, 518 

measurement of, 866 
Perry, John, his meter. 442 
Persistence (see Time-constant) 
Phase, 470, 472 

Phosphorescence caused by dis- 
charge, 320, 321 
Photo-chemical excitation, 530 
Photographic plate affected by dis- 
charge, 324 
Photophone, 529 
Photo-voltaic property of selenium, 

529 
Physiological actions, 254, 325 
Piercing glass, prevention of, 62 
Piezo-electricity, 75 
Plane, the proof-, 32 

" for magnetism, 232 

Plante, Gaston, secondary cells, 492 

globular hghtning, 331 
Plants, electricity of, 77, 256 
Plate condenser,'^56, 295, 304 

electrical machine, 43 
Platinoid, 404 
PlUcJcer. Julius, on diamagnetism, 

etc., 370, 373 
Poggendorff, J. C, his cell, 180 

method of measuring E.M.F., 
416 
Points, density of charge on, 38, 274 

discharge at, 42, 45, 46, 47, 274, 
329 
Poisson, magne-crystallic action, 

373 
Polarity, diamagnetic, 369 

magnetic, 90, 116, 126 
Polarization (electrolytic) in battery 
cells, 175, 487 

of Voltameter, 487, 492 

remedies for, 180 

rotation of plane of, 526 et seg. 
Polarized mechanism, 387 

relay, 501 
Poles of magnets, 86, 134 

of pj'-roelectric crystals, 74 

of voltaic battery, 168 
Polyphase currents, 485 
Porous cell, 180 
Porret's phenomenon, 250 
Portable electrometer, 287 
Portative force, 114 



Post-Office Bridge, 415 

relay, 501 
Positive and negative electrification, 

5, 327 
Potential, electric, 40, 263 

zero, 40, 264 
of conducting sphere, 269 
galvanometers, 220 
magnetic, 337, 347, 348 

" due to current, 351 
mutual, of two circuits, 352, 
357 
Potential-divider nul method, 418 
Potentiometer, 416 
Pouillet, Claude S. M., sine galvan- 
ometer, 214 
tangent galvanometer, 212 
Powdered meftals, conduction of, 
400 
sensitiveness to sparks, 521 
Powders, electroscopic, 31, 47, 299, 

324 
Power, 435 

transmission of, 447 
Power-houses, 440 
Poynting. John Henry, on energy- 
paths, 519 
Practical units, 354 
Preece, William Henry, telegraphy, 

497 
Pressure produces electrification, 75 
effect on electrolysis, 490 
(voltage), 169 
Priestley, Joseph, on electric ex- 
pansion, 300 
on influence, 26 (footnote) 
Prime conductor, 42 
Printing telegraphs, 497 
Proof-plane, 32 

magnetic, 232 
Protoplasm, electric property of, 256 
Pyroelectricity, 74 
Pyrometer, 404 

QuADEANT electrometer (Lord Kel- 
vin's), 288 
electroscope (Henley's), 17 
Quadruplex telegraphy, 508 
"Quantity" arrangement of cells, 
etc., 192, 40'7 
of electricity, unit of, 21, 262, 
354 
Quartz fibre, 299 
Quartz, no residual charge from, 299 

as insulator, 80, 299 
Quetelet, E., on atmospheric elec- 
tricity, 333, 335 



624 



ELECTRICITY AND MAGXETISM 



The Xwnhers refer to the Xurahered Paragraphs. 



Quincke. Georg, on diaphragm 
ciurents, 252 
on electric expansion, 300 
on electro-optic phenomena, 
525 
Quinine, use of, for mapping fields, 



Eai)ia>"t state of matter, 321 

Eadio-micrometer, 425 

Eate of chansre of current, 454, 4T2 

(footnote) 
Eatio of' electrostatic to electro- 
magnet units, 253, 359 
Eay. electric (torpedo), 76 
Eays. kathodic, 321 

cun-ent balance. 396 
Bayleigh. Lord, determination of 

ohm, 35S 
Eeactance, 473 
Eeciprocal accumulation. 49 
Eecording instruments. 160, 334 
Eedistribution of charge, 39 
Eeduction of metals, 494 
Eetiecting galvanometer, 215 
Eeflexion o1f electric waves, 520 
Eefractive index, 515 
Eegistering magnetographs and elec- 
trometers, 160, 334 
Reis, Philipp. invention of tele- 
phone, 510 
Eelays. 501 
Eeluctance. 375 
Eeluctivity, 375 (footnote) 
Eemanence, 367 
Eeplenisher. 49, 257, 253 
Eepulsion and attraction of electri- 
fied bodies, 2, 4, 22, 24, 74, 262 
and attraction, experiments 

on, 47 
and attraction of currents, 

33S, 359, 394 
and atti-action of magnets, 84, 
S3 
Eeptilsion electrometers, 256 
Eesidual charge of Levden jar, 61. 

299 
Eesidual charge of cable, 301 

of Voltameter, 492 
magnetism. 112. 127, 367 
Eesinous electricity, 5 
Eesistance and heat, 426 
Eesistance. 30, 171. 400. 426 

affected by temperature, 404 
light, 529 
" magnetism, 397 

" sound, 512 



Eesistance. as a velocity, 357 

bridge or balance", 413 

coils. 414 

Internal, of cell, 192, 407, 417 

internal, of cell, measurement 
of. 417 

laws of, 400 

magnetic. 375 

measurement of. 411 et seq. 

of gases. 171, 322 

of glow lamps, 452 

of human bodv, 255 

of liquids. 171," 403 

of vacuum, 321 

specific. 403 

to alternate currents, 476 

units of. 352 et seq. 
Eesistivity. 402 
Eesonance. 517 
Eesonator. 520 

Eesultant magnetic force. 115 
Eetardation "of cun-ents through 

cables. 301. 323, 505 
Eetentivity (magnetic\ 95. 367 
Eeturn shock or stroke, 29. 331 
Eeversal of influence machines, 53 
Eeversibilitv of processes in circuit. 

245. 436 
Eeversing-switch. 230, 495 
Eeymond. Du BoU, his galvan- 
ometer. 257 

on animal electricity. 257 

tmpolarizable electrodes. 257 
Eheostats, 400 
Eheometer. ") 

Eheoscope, v see footnote to 203 
Eheotrope. j 

Riess. Peter, on electric distribution, 
35 

on length of spark, 313 

electric thermometer, 317 
Ritchie, magnetic circuit, 375 

his motor, 443 
Ritter. Johann Wilhelm. on action 
of current on sight, 254 

his secondary pile, 492 ■ 

on subjective eralvanic sounds, 
254 

on the sensitive plant, 256 
Eolling fi-iction. 12, 73 
Romagnosi. Dr.. discovers magnetic 

action of current. 195 
Romas, De, his electi-ic kite, 329 
Ronalds. Sir Francis, invented a 

telegraph, 497 
Eotation of plane of polarization, 
526 



INDEX 



625 



The Xumhers refer to the Xumbered Paragraphs. 



Kotations, electromagnetic, 393 

Arago's, 45T 
Kotatory magnetic field, 4S5 
Eoughness of surface as depolarizer, 

ISO 
Ilowland, Henry A., on magnetic 
effect of electric convexion, 
397 
on magnetic circuit, 3T5 
Bucker, Arthur William, on ration- 
alization of dimensions, 360 
Riicker and Tliorpe, magnetic sur- 
vey, 154 
Ruhmkorff's electromagnet, 369 
induction coil, 229 
coil, mutual induction of, 454 

St. Elmo's Fire, 329 {footnote) 
Safetv-fuses, 429 
Salts." electrolysis of, 238, 490 
Sanderson, J. Burdon, on electric 
sensitiveness of carnivorous 
plants, 256 
Saturation, magnetic, 112, 363 et seq. 
Savery. S5 
Sawdust battery, 187 
Schallenberger's meter, 442 
Schuckert, ammeter, 221 
Schuster, Arthur, on electrolysis of 

gases, 322 
Schiveigger's multiplier, 200 
Screening, magnetic, 96 
inductive, 514 
of eddy-currents, 457, 514 
Secohm, 453 
Secondary actions in electrolysis, 

490 
Secondarj^ batteries, 492 
Secular variations of magnetic ele- 
ments, 155 
Seebeck, Thojuas Johann, effect, 

419 
Selenium, photo-electric properties 
of, 529 
resista^nce of, 403 {table), 529 
: Self-exciting influence machine, 50 

dynamo, 462 
Self-induction, 458, 472 

in electric discharge, 515 
Self-recording instruments, 160, 334 
Semaphore, Henley's, 17 
Sensitive plant, behaviour of, 256 
.Series, arc lamps in, 45*} 
capacities in, 308 
cells in, 168, 406 
dynamos, 465 
resistances in, 406 

2 S 



Serrin, Victor, his lamp, 449 
Shadows, electric, 47 

in partial vacuum, 321 
Sheet conductor, flow of electricity 

in, 410 
Shell, magnetic, 118, 203, 350 

potential due to, 348 
Shielding, magnetic, 97 
Shock, electric, 254, 325 
Shunt, 215, 409 

coil in arc lamps, 449 

dynamo, 465 
Shuttle armature, 461 
Siemens, Alexander, on length of 

spark, 318 
Siemens, Werner, on dynamos, 
461 
■mercury unit, 358 

electrodynamometer, 395 

shuttle-wound armature, 461 

heating in Leyden jar, 299 
Sight affected by current, 254 
Silurus, the, 76 
Sine galvanometer, 214 
Sine law, 476 
Single-fluid cells, 180 
Single-needle instrument, 498 
Single touch, 100 
Siphon recorder, 506 
Skew-symmetry of crj'stals, T5 
Skin effect, 476 
Skin, E.M.F. in the, 257 
Smee, Alfred, his Battery, ISO 
Smith, Frederick John, effect on 

photographic plate, 324 
Smith, Willoughby, on selenium, 

529 
Soap-bubble, electrified, 4 
Sodium by electrolysis, 490 
Solenoid arc lamps, 449 
Solenoid, 385 

magnetizing force of, 341 
Solid angles, 148 (Appendix A) 
Solidification, 69 

Sound of magnetization, 124, 510 
Sounder, the, 497 
Sources of electricity, 12, 65 
Spark, 11, 46, 47, 310 

duration of, 323 

length of, 48, 313, 329 
Sparking at commutator, 463 
Specific resistance, 403 

inductive capacity, 25, 56, 295, 
299 
Speed of motor, 444 

of signalling, 301, 302, 323 



626 



ELECTRICITY AND MAGNETISM 



The Numbers refer to the Xumhered Paragraphs. 



Sphere, distribution of charge over, 
38, 273 et seq. 

potential of, 2m, 271 

capacity of, 271 
Spiral shortens itself, 390 
Spottiswoode, William, on striae, 

322 
Square root of mean square, 471 
Standard cells, ISS 

effect of temperature on, 194 
Standards, 354 
Steel hardening, 108 
Steel, properties of, 362 

facing, 495 
Stewart, Balfour, on atmospheric 
electricity, 335 

on magnetic storms, 158 
Storms, magnetic, 159 
Straight conductor force near, 207, 

343 
Strain, dielectric, 64, 299, 525 
Strength of current, 171, 190, 354 

of current in magnetic mea- 
sure, 206, 207, 353 et seq. 

of dielectric, 299, 311 

of magnet pole, 112, 352 

of magnetic shell, 348 
Stress, electric, 13, 16, 20, 22, 24, 63, 
279, 299, 311, 525 

electric, optical effect of, 525 

magnetic, 119, 340, 389 
Strife in vacuum tubes, 320, 322 
Sturgeon, William, his commuta- 
tor, 461 

electro-magnets, 3S1 

on magnetic circuit, 875 

induction coil, 229 
Submarine telegraphs, 504 
Sucking-magnet, 385 
Sulphur as depolarizer, 185 
Sulphuretted hydrogen, iron nega- 
tive to copper in, 80 
Sulzer's experiment, 254 
Supph' meters, 442 
Surface contact, 12 

density of charge, 38, 273 

limit of, 273 

of magnetism, 134, 337 
Surgical applications, 258 
Susceptibility, 365 
Suspended-coil galvanometers, 216 
Swammerdam's frog experiment, 

255 
Swan's incandescent lamp, 452i 
Symmer, on two kinds of electrifica- 
tion, 5 
Synchronizing, 479 



Tait, Peter Guthrie, electrifica- 
tion by evaporation of sul- 
phate of copper solution, 71 
heating of iron electrode, 433 
thermo-electric diagram, 424 
Tangent galvanometer, 212 

of angle of lag, 473 
Tapper, 498 

Taste affected by current, 254 
Telegraph, electric, 497 

Bain's chemical, 246 
Alorse's instrument, 499 
needle instrument, 498 
Telegraphy, diplex, 503 
duplex, 503 
quadruplex, 503 
submarine, 504 
Telephone, Philipp Reis's, 510 
currents of. 255 
Dolbear's. 299, 511 
Edison's (carbon), 511 
Graham Bell's (articulating), 

510 
Varley's (condenser), 299, 511 
Exchanges, 513 
Temperature affects resistance, 194, 
404 
affected by resistance, 426 
effect on length of spark, 313- 

314 
of the arc, 448 
Temperins- of steel, 108 
Tension, electric, 13, 16, 20, 22, 24, 
63, 273 (footnote), 279, 299, 
311, 525 
Terquem, A., parrot-cage experi- 
ment, 34 
Terrestrial Magnetism, 95, 150, 361, 

365 
Test for weak currents (chemical), 
246, 316 
for weak currents (physiologi- 
cal), 255 
Testing for taults, 502 
Tetanization produced by inter- 
rupted currents, 256 
Theories of Electricity, 7, 327, and 

Preface, ix 
Theories of Magnetism, 99, 126 

Aynpere's, 398 
" Ewing's. 127 
" Maxicell's, 126 
Weber's, 126, 127 
Theory of Electrolysis, Grotthuss's 

and Clausius's, 491 
Theorv of Earth's magnetism, 161 
of Light, 518 



INDEX 



627 



The Xumhers refer to the Nurahered Paragraphs. 



Thermo-electric currents, Ko A^a 
Thermo-electricitj-, p^*, -iia 

Thermo-electric Diagram, 424 
Thermo-electi'omotive Series, 424 
Thermopile, 425 

Thompson, Silvanus Phillips, on 
magnetic figures due to cur- 
rents, 202, 3S9 
on positive and negative 

states, 32T 
on opacity of tourmaline, 518 
Thomson, Joseph J., on Contact 
Electricity, 81 
on conducti\ity of gases, 
322 
Thomson, Sir William (see Kelvin, 
Lord) 
effect. 424 
Thomson, Elihii, his meter, 442 

on alternate-current magnets, 

4T7 
on welding, 433 
Thomson- Houston dynamos, 468, 

4TS 
Thorpe and HucJcer, magnetic sur- 
vey, 154 
Three wire svstem, 453 
Thunder, 11,' 331 
Thunderstorms, 329 
Theory of, 330 
Time-constant, 460 
Tinfoil Condensers, 55, 302 
Tivoli, transmission of power from, 

447 
Toepler, A., his Influence Machine, 

51 
Tongs. Discharging, 59 
Torpedo (electric fish), 76, 246 
Torpedoes, fuzes for firing, 316, 

432 
Torque. 136 
Torque of motor, 444 
Torsion affected by magnetization, 

124 
Torsion Balance, or ) Coulomb's, 
Torsion Electrometer, f 18, 182 
Torsion method, 209, 210 
Tourmaline, 74, 324, 518 
Transformers, 228, 430 

for vacuum tubes, 320 
Transmission of power, 447, 479 
Tri-phase, 4S5 

Trolley wheel for tramcars, 446 
Trowbridge, on magnetization at 

-lOO^C, 111 
Tube of force, 337 (g) 
Tuning-fork method, 418 



Two-fluid cells, 181 

theory, 7 
Two kinds of Electrification, 5, 6 
" Magnetic poles, 89 
Tyndall, John, diamagnetic polarity, 
372 
magne-crystallic action, 373 



Ultra-gaseous matter, 321 
Ultra-violet waves, 313 

discharge by, 531 

effect on metal, 531 
Unit, Board of Trade, 440, 488 
Unit jar, 285 

Units and standards. Board of Trade 
(see Appendix B) 

electromagnetic, 352 et seq. 

electrostatic, 283 et seq. 

fundamental and derived, 281, 
282 

ratio of electrostatic to electro- 
magnetic, 262 (footnote), 
283, 359 
Unipolar Machines, 469 
Universal Discharger, 62 
Unvarjang magnets, 110 
Upward, his cell, 193 
Ure, Dr., on animal electricity, 255 



"v,"359, 518 

Vacuum, induction takes place 
through, 64, 96, 97 
partial, spark in, 11, 320 
spark wiU not pass through, 

313, 321 
tubes, 320, 321 
" Variation," the (see Declination) 
Variation of Declination and Dip — 
annual, 157 
diurnal, 156 
geographical, 151, 154 
secular, 155 

of electrification of the atmos- 
phere. 335 
Farley, Cromwell Fleetwood, his 
galvanometer, 316 
on capacity of polarization, 

492 
telegraph, 497 
Farley, Samuel Alfred, his tele- 
phone, 299, 510 
early dynamo, 462 
Vegetables, Electricity of, 77 

carnivorous, sensitiveness of, 
256 



628 



ELECTRICITY AND MAGNETISM 



The Numhei'S refer to the Xumbered Paragraphs. 



Velocity- of discharge. 323 

of light, 359, 51 S 

of electric wayes, 518 

of rubbing, electrification de- 
pends on, 73 

resistance as a, 357 
Verdet's constant, 526 
Vibration produces Electrification. 

67 
Vibrator for measuring capacity, 41S 
Villari, Emilio, effect of tension, 

364 
Violet waves (see Ultra-violet) 
A'irtual volts and amperes, 471 
Vitreous electricity, 5 
Volt. 169, 3.W 

Volta, Alessandro, his Electro- 
phorus, 26 

Condensing Electroscope, 79 

Contact Series, SO 

Cro^vn of Cups, 165 

on Atmospheric Electricity, 
334 

on Contact Electricity, 79, 163 

on Electric Expansion, 300 

on Electrification due to com- 
bustion, 70 

Subjective Sounds due to Cur- 
rent. 254 

Volta s Law, SO, 163. 170 

Voltaic Pile. 164 
Voltaic Electricity (see Current 
Electricity) 

arc, 44S 

battery, 16S, 178; pUe, 164 

cell, simple, 166 
Voltameter. 242. 243, 244, 4S7 
Voltmeter. 220 

Car dew's, 430 

electrostatic, 290 
Voss machine. 51 



Walker. Charles V., used sulphur 

in cell, 1:?5 
Warburg. E., on hysteresis, 368 
Water. Electrolysis of, 235, 4S7 
TVater-dropping, discharge by, 334 
Watt, the, 354, 435 
Wattmeter, 438 
Watts, true and apparent, 475 



Waves, electric, 515 
Weber, the. 354 

Weber, Wilhelm, the Electro-dyna- 
mometer, 394 
on diamagnetic polaritj', 372 
evaluation of ohm, 358 
of "V,'' 359 
theory of magnetism, 126, 127 
Welding, 433 

Weston. Edivard, voltmeter, 220 
standard cell, 188 
temperature coefficient of 
alloys, 404 
Wheatston'e. Sir Charles, on the 
brush discharge, 319 
Automatic Telegraph. 497 
Dynamo - electric Machines, 

462 
on supposed velocity of elec- 
tricity. 323 
JVheatstone' s Bridge or Bal- 
ance, 413 
Whirls, magnetic. 202, 389 
Wiedemann. Gustav, on effect of 
magnetism on torsion. 124 
diamagnetism, 370 {footnote) 
Wilde. Henry, Magneto - electric 

Machine. 462 
Wilcke, A., electrophorus, 26 (foot- 
note) 
Wimshursi, James, Influence ma- 
chine, 52 
Wind, electric, 47, 324 
Winding of electromagnets, 375 et 
seq., 885, 386 (and see p. 
596) 
Window, aluminum, 321 
Wohlers cell. 193 
Wollastons Battery, 180 
Work by conductor cutting lines, 

339 
Wrobleicski, resistance of, at low 
temperatures, 404 

ZAMBOxrs Dry Pile, 16, 193, 291 

Zanotti, experiment on grass- 
hopper, 255 

Zero potential, 40, 264 

Zero of temperature, resistance near, 
404 

Zinc as fuel, 166 



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